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residual","TFP"],"papers":21,"papers_7d":1,"page":true},{"rank":25,"name":"Random forest","slug":"random-forest","latex":"\\hat f(x) = \\frac{1}{B}\\sum_{b=1}^{B} T_b(x)","area":"Machine learning","about":"Averages many decision trees grown on bootstrap samples with random feature subsets.","names":["random forest"],"papers":20,"papers_7d":4,"page":true},{"rank":26,"name":"ARIMA","slug":"arima","latex":"\\phi(L)\\,(1 - L)^{d}\\, y_t = \\theta(L)\\,\\varepsilon_t","area":"Time series","about":"Autoregressive integrated moving-average model of a time series, with lag operator L and differencing order d.","names":["ARIMA","SARIMA","ARMA","ARFIMA","autoregressive integrated moving average","autoregressive moving average"],"papers":19,"papers_7d":2,"page":true},{"rank":26,"name":"Autoregressive distributed lag (ARDL)","slug":"autoregressive-distributed-lag-ardl","latex":"y_t = \\alpha + \\sum_{i=1}^{p}\\phi_i\\, y_{t-i} + \\sum_{j=0}^{q}\\beta_j^\\top x_{t-j} + \\varepsilon_t","area":"Time series","about":"Regresses a series on its own lags and current and lagged regressors; the bounds test checks for a long-run relation.","names":["autoregressive distributed lag","ARDL","NARDL","QARDL","CS-ARDL"],"papers":19,"papers_7d":1,"page":true},{"rank":28,"name":"Granger causality","slug":"granger-causality","latex":"y_t = \\sum_{i=1}^{p} a_i\\, y_{t-i} + \\sum_{j=1}^{p} b_j\\, x_{t-j} + \\varepsilon_t,\\quad H_0: b_1 = \\dots = b_p = 0","area":"Time series","about":"Tests whether past values of x help predict y beyond y's own past.","names":["Granger causality","Granger cause","Granger causal","Granger non-causality"],"papers":16,"papers_7d":1,"page":true},{"rank":28,"name":"Regression discontinuity design","slug":"regression-discontinuity-design","latex":"\\tau = \\lim_{x \\downarrow c} E[Y \\mid X = x] - \\lim_{x \\uparrow c} E[Y \\mid X = x]","area":"Causal inference","about":"Estimates an effect from the jump in outcomes at a cutoff c of a running variable X that decides treatment.","names":["regression discontinuity","RDD"],"papers":16,"papers_7d":0,"page":true},{"rank":30,"name":"Gini coefficient","slug":"gini-coefficient","latex":"G = \\frac{\\sum_{i=1}^{n}\\sum_{j=1}^{n} \\lvert x_i - x_j \\rvert}{2 n^2 \\bar x}","area":"Labour, inequality and competition","about":"Inequality measure from 0 (equal) to 1 (one unit has everything).","names":["Gini coefficient","Gini index"],"papers":15,"papers_7d":1,"page":true},{"rank":31,"name":"Markov-switching model","slug":"markov-switching-model","latex":"y_t = \\mu_{s_t} + \\varepsilon_t,\\quad \\Pr(s_t = j \\mid s_{t-1} = i) = p_{ij}","area":"Time series","about":"Lets a model's parameters change with an unobserved regime that follows a Markov chain.","names":["Markov switching","Markov regime switching","regime switching model"],"papers":13,"papers_7d":1,"page":true},{"rank":31,"name":"Spatial autoregressive models (spatial Durbin)","slug":"spatial-autoregressive-models-spatial-durbin","latex":"y = \\rho\\, W y + X\\beta + W X\\theta + \\varepsilon","area":"Regression models","about":"Lets outcomes and regressors of neighbouring units, weighted by a spatial matrix W, affect each unit.","names":["spatial Durbin","spatial autoregressive model","spatial lag model","spatial error model","spatial econometric"],"papers":13,"papers_7d":1,"page":true},{"rank":33,"name":"Support vector machine (SVM)","slug":"support-vector-machine-svm","latex":"\\min_{w, b, \\xi}\\ \\tfrac{1}{2}\\lVert w \\rVert^2 + C \\sum_i \\xi_i\\ \\ \\text{s.t.}\\ \\ y_i (w^\\top x_i + b) \\ge 1 - \\xi_i,\\ \\xi_i \\ge 0","area":"Machine learning","about":"Finds the separating hyperplane with the widest margin; support vector regression adapts it to regression.","names":["support vector machine","support vector regression","SVM","SVR"],"papers":12,"papers_7d":1,"page":true},{"rank":34,"name":"Event study (abnormal returns)","slug":"event-study-abnormal-returns","latex":"AR_{it} = R_{it} - (\\hat\\alpha_i + \\hat\\beta_i R_{mt}),\\quad CAR_i = \\sum_{t=t_1}^{t_2} AR_{it}","area":"Causal inference","about":"Measures returns beyond what a market model predicts around an event such as an announcement.","names":["abnormal return","cumulative abnormal return","buy-and-hold abnormal return"],"papers":11,"papers_7d":1,"page":true},{"rank":34,"name":"Herfindahl-Hirschman index","slug":"herfindahl-hirschman-index","latex":"\\mathit{HHI} = \\sum_{i=1}^{N} s_i^2","area":"Labour, inequality and competition","about":"Market concentration as the sum of squared market shares.","names":["Herfindahl","HHI"],"papers":11,"papers_7d":0,"page":true},{"rank":36,"name":"Value at risk (VaR)","slug":"value-at-risk-var","latex":"\\mathrm{VaR}_\\alpha(L) = \\inf\\{\\ell \\in \\mathbb{R} : \\Pr(L > \\ell) \\le 1 - \\alpha\\}","area":"Asset pricing and risk","about":"The loss that is exceeded with probability at most 1 - alpha over a given horizon.","names":["value at risk","VaR"],"papers":10,"papers_7d":1,"page":true},{"rank":37,"name":"Expected shortfall (CVaR)","slug":"expected-shortfall-cvar","latex":"\\mathrm{ES}_\\alpha(L) = \\frac{1}{1 - \\alpha}\\int_\\alpha^{1} \\mathrm{VaR}_u(L)\\,du","area":"Asset pricing and risk","about":"Average loss in the worst 1 - alpha share of outcomes; also called conditional value at risk.","names":["expected shortfall","conditional value at risk","CVaR"],"papers":9,"papers_7d":0,"page":true},{"rank":37,"name":"Nash equilibrium","slug":"nash-equilibrium","latex":"u_i(s_i^{*}, s_{-i}^{*}) \\ge u_i(s_i, s_{-i}^{*})\\quad \\forall i,\\ \\forall s_i","area":"Game theory and decision analysis","about":"No player can gain by changing strategy alone.","names":["Nash equilibrium","Nash equilibria"],"papers":9,"papers_7d":0,"page":true},{"rank":37,"name":"Synthetic control method","slug":"synthetic-control-method","latex":"\\hat Y^{N}_{1t} = \\sum_{j=2}^{J+1} w_j^{*}\\, Y_{jt},\\quad w_j^{*} \\ge 0,\\ \\sum_j w_j^{*} = 1","area":"Causal inference","about":"Builds the counterfactual for a treated unit as a weighted average of untreated units.","names":["synthetic control"],"papers":9,"papers_7d":0,"page":true},{"rank":40,"name":"Data envelopment analysis (DEA)","slug":"data-envelopment-analysis-dea","latex":"\\max_{u, v}\\ \\frac{\\sum_r u_r\\, y_{r0}}{\\sum_i v_i\\, x_{i0}}\\ \\ \\text{s.t.}\\ \\ \\frac{\\sum_r u_r\\, y_{rj}}{\\sum_i v_i\\, x_{ij}} \\le 1\\ \\ \\forall j","area":"Efficiency and operations","about":"Scores the efficiency of each unit as its best ratio of weighted outputs to weighted inputs relative to all units.","names":["data envelopment analysis","DEA model","super-efficiency DEA","slacks-based measure","SBM model","network DEA","DEA"],"papers":8,"papers_7d":0,"page":true},{"rank":40,"name":"Gradient descent","slug":"gradient-descent","latex":"\\theta_{t+1} = \\theta_t - \\eta\\, \\nabla_\\theta \\mathcal{L}(\\theta_t)","area":"Machine learning","about":"Moves parameters a step against the gradient of the loss; stochastic gradient descent uses mini-batches.","names":["gradient descent","SGD"],"papers":8,"papers_7d":2,"page":true},{"rank":40,"name":"Heckman selection model","slug":"heckman-selection-model","latex":"E[y_i \\mid x_i, s_i = 1] = x_i^\\top\\beta + \\rho\\,\\sigma_\\varepsilon\\,\\lambda(z_i^\\top\\gamma),\\quad \\lambda(\\cdot) = \\frac{\\phi(\\cdot)}{\\Phi(\\cdot)}","area":"Causal inference","about":"Corrects for non-random selection of the observed sample with the inverse Mills ratio from a first-stage probit.","names":["Heckman selection","Heckman two-step","Heckman two-stage","Heckman correction","Heckman model","inverse Mills ratio","sample selection model"],"papers":8,"papers_7d":1,"page":true},{"rank":40,"name":"Principal component analysis (PCA)","slug":"principal-component-analysis-pca","latex":"\\max_{\\lVert w \\rVert = 1}\\ w^\\top \\Sigma\\, w","area":"Machine learning","about":"Finds the orthogonal directions of largest variance in the data.","names":["principal component analysis","principal components analysis","PCA"],"papers":8,"papers_7d":1,"page":true},{"rank":40,"name":"Q-learning","slug":"q-learning","latex":"Q(s, a) \\leftarrow Q(s, a) + \\alpha\\big[r + \\gamma \\max_{a'} Q(s', a') - Q(s, a)\\big]","area":"Machine learning","about":"Reinforcement learning of action values from rewards; deep Q-networks approximate Q with a neural network.","names":["Q-learning","deep Q-network","DQN"],"papers":8,"papers_7d":1,"page":true},{"rank":40,"name":"Sharpe ratio","slug":"sharpe-ratio","latex":"S_p = \\frac{E[R_p] - R_f}{\\sigma_p}","area":"Asset pricing and risk","about":"Excess return of a portfolio per unit of total risk.","names":["Sharpe ratio"],"papers":8,"papers_7d":2,"page":true},{"rank":46,"name":"Kalman filter","slug":"kalman-filter","latex":"\\hat x_{t \\mid t} = \\hat x_{t \\mid t-1} + K_t\\,(y_t - H\\,\\hat x_{t \\mid t-1})","area":"Time series","about":"Recursively updates estimates of an unobserved state from noisy observations.","names":["Kalman filter","Kalman filtering","Kalman smoother"],"papers":7,"papers_7d":0,"page":true},{"rank":47,"name":"Denoising diffusion model","slug":"denoising-diffusion-model","latex":"\\mathcal{L} = E_{t, x_0, \\epsilon}\\Big[\\left\\lVert \\epsilon - \\epsilon_\\theta\\big(\\sqrt{\\bar\\alpha_t}\\, x_0 + \\sqrt{1 - \\bar\\alpha_t}\\, \\epsilon,\\ t\\big) \\right\\rVert^2\\Big]","area":"Machine learning","about":"Generative model that learns to remove noise step by step; the basis of current image generators.","names":["denoising diffusion","diffusion probabilistic","latent diffusion","score-based generative","Stable Diffusion"],"papers":6,"papers_7d":0,"page":true},{"rank":47,"name":"Low-rank adaptation (LoRA)","slug":"low-rank-adaptation-lora","latex":"W = W_0 + B A,\\quad B \\in \\mathbb{R}^{d \\times r},\\ A \\in \\mathbb{R}^{r \\times k},\\ r \\ll \\min(d, k)","area":"Machine learning","about":"Fine-tunes a large model by learning a small low-rank update to its weights.","names":["low-rank adaptation","LoRA"],"papers":6,"papers_7d":0,"page":true},{"rank":47,"name":"Proximal policy optimization (PPO)","slug":"proximal-policy-optimization-ppo","latex":"L(\\theta) = E_t\\big[\\min\\big(r_t(\\theta)\\hat A_t,\\ \\mathrm{clip}(r_t(\\theta), 1 - \\epsilon, 1 + \\epsilon)\\,\\hat A_t\\big)\\big]","area":"Machine learning","about":"Policy-gradient reinforcement learning with a clipped objective that keeps updates small.","names":["proximal policy optimization","proximal policy optimisation","PPO"],"papers":6,"papers_7d":0,"page":true},{"rank":47,"name":"Variational autoencoder (ELBO)","slug":"variational-autoencoder-elbo","latex":"\\log p_\\theta(x) \\ge E_{q_\\phi(z \\mid x)}\\big[\\log p_\\theta(x \\mid z)\\big] - D_{\\mathrm{KL}}\\big(q_\\phi(z \\mid x) \\parallel p(z)\\big)","area":"Machine learning","about":"Generative model trained by maximizing the evidence lower bound on the data likelihood.","names":["variational autoencoder","variational auto-encoder","evidence lower bound","ELBO","VAE"],"papers":6,"papers_7d":1,"page":true},{"rank":51,"name":"Gated recurrent unit (GRU)","slug":"gated-recurrent-unit-gru","latex":"h_t = (1 - z_t) \\odot h_{t-1} + z_t \\odot \\tilde h_t","area":"Machine learning","about":"A simpler gated recurrent cell with update and reset gates.","names":["gated recurrent unit","GRU"],"papers":5,"papers_7d":0,"page":true},{"rank":51,"name":"Generative adversarial network (GAN)","slug":"generative-adversarial-network-gan","latex":"\\min_G \\max_D\\ E_x\\big[\\log D(x)\\big] + E_z\\big[\\log\\big(1 - D(G(z))\\big)\\big]","area":"Machine learning","about":"A generator and a discriminator trained against each other.","names":["generative adversarial","GAN"],"papers":5,"papers_7d":0,"page":true},{"rank":51,"name":"k-means clustering","slug":"k-means-clustering","latex":"\\min_{C_1, \\dots, C_k} \\sum_{j=1}^{k} \\sum_{x \\in C_j} \\lVert x - \\mu_j \\rVert^2","area":"Machine learning","about":"Partitions observations into k clusters around their means.","names":["k-means"],"papers":5,"papers_7d":1,"page":true},{"rank":54,"name":"Kullback-Leibler divergence","slug":"kullback-leibler-divergence","latex":"D_{\\mathrm{KL}}(P \\parallel Q) = \\sum_x P(x) \\log \\frac{P(x)}{Q(x)}","area":"Machine learning","about":"How much one probability distribution differs from another.","names":["Kullback-Leibler","KL divergence"],"papers":4,"papers_7d":0,"page":true},{"rank":55,"name":"Analytic hierarchy process (AHP)","slug":"analytic-hierarchy-process-ahp","latex":"A\\, w = \\lambda_{\\max}\\, w,\\quad CR = \\frac{(\\lambda_{\\max} - n)/(n - 1)}{RI}","area":"Game theory and decision analysis","about":"Derives criteria weights from pairwise comparisons; CR checks their consistency.","names":["analytic hierarchy process","analytical hierarchy process","AHP"],"papers":3,"papers_7d":0,"page":true},{"rank":55,"name":"Cox proportional hazards model","slug":"cox-proportional-hazards-model","latex":"h(t \\mid x) = h_0(t)\\,\\exp(x^\\top\\beta)","area":"Regression models","about":"Models the hazard of an event over time as a baseline hazard scaled by the regressors.","names":["Cox proportional hazard","proportional hazards model","Cox regression","Cox model","Cox hazard model"],"papers":3,"papers_7d":0,"page":true},{"rank":55,"name":"Gravity model of trade","slug":"gravity-model-of-trade","latex":"X_{ij} = G\\,\\frac{Y_i^{\\beta_1}\\, Y_j^{\\beta_2}}{D_{ij}^{\\beta_3}}","area":"Growth, trade and environment","about":"Trade between two countries rises with their economic size and falls with the distance between them.","names":["gravity model","gravity equation","structural gravity","PPML"],"papers":3,"papers_7d":0,"page":true},{"rank":55,"name":"Mean-variance portfolio (Markowitz)","slug":"mean-variance-portfolio-markowitz","latex":"\\min_{w}\\ w^\\top \\Sigma\\, w\\ \\ \\text{s.t.}\\ \\ w^\\top \\mu = \\mu_p,\\ \\ w^\\top \\mathbf{1} = 1","area":"Asset pricing and risk","about":"Chooses portfolio weights with the lowest variance for a target expected return.","names":["mean-variance","Markowitz","modern portfolio theory"],"papers":3,"papers_7d":0,"page":true},{"rank":55,"name":"New Keynesian Phillips curve","slug":"new-keynesian-phillips-curve","latex":"\\pi_t = \\beta\\,E_t[\\pi_{t+1}] + \\kappa\\, x_t","area":"Macroeconomics","about":"Links inflation to expected future inflation and the output gap (or real marginal cost) x.","names":["Phillips curve"],"papers":3,"papers_7d":0,"page":true},{"rank":55,"name":"TOPSIS","slug":"topsis","latex":"C_i = \\frac{d_i^{-}}{d_i^{+} + d_i^{-}}","area":"Game theory and decision analysis","about":"Ranks alternatives by closeness to the ideal solution and distance from the worst one.","names":["TOPSIS"],"papers":3,"papers_7d":1,"page":true},{"rank":61,"name":"Amihud illiquidity ratio","slug":"amihud-illiquidity-ratio","latex":"\\mathit{ILLIQ}_i = \\frac{1}{D_i}\\sum_{d=1}^{D_i}\\frac{\\lvert R_{id} \\rvert}{\\mathit{DVOL}_{id}}","area":"Asset pricing and risk","about":"Average absolute daily return per dollar of trading volume: the price impact of trading.","names":["Amihud illiquidity","Amihud's illiquidity","Amihud measure","Amihud's measure","Amihud ratio"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Bellman equation","slug":"bellman-equation","latex":"V(s) = \\max_{a}\\left\\{ r(s, a) + \\beta \\sum_{s'} P(s' \\mid s, a)\\, V(s') \\right\\}","area":"Game theory and decision analysis","about":"Recursive condition for the value of a dynamic optimization or Markov decision problem.","names":["Bellman equation","Hamilton-Jacobi-Bellman","HJB equation","Bellman optimality"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Capital asset pricing model (CAPM)","slug":"capital-asset-pricing-model-capm","latex":"E[R_i] = R_f + \\beta_i\\,(E[R_m] - R_f)","area":"Asset pricing and risk","about":"Expected return of an asset as the risk-free rate plus its market beta times the market risk premium.","names":["capital asset pricing model","CAPM"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Carhart four-factor model","slug":"carhart-four-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + m_i\\,\\mathit{UMD}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds a momentum factor (UMD) to the Fama-French three factors; widely used for fund performance.","names":["Carhart four-factor","Carhart 4-factor","Carhart model","four-factor model"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Dechow-Dichev accruals quality","slug":"dechow-dichev-accruals-quality","latex":"\\Delta WC_{it} = \\beta_0 + \\beta_1\\, CFO_{i,t-1} + \\beta_2\\, CFO_{it} + \\beta_3\\, CFO_{i,t+1} + \\varepsilon_{it}","area":"Accounting","about":"Measures how well working-capital accruals map into past, current and future cash flows.","names":["Dechow and Dichev","Dechow-Dichev","accruals quality","accrual quality"],"papers":2,"papers_7d":1,"page":true},{"rank":61,"name":"Fama-French five-factor model","slug":"fama-french-five-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + r_i\\,\\mathit{RMW}_t + c_i\\,\\mathit{CMA}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds profitability (RMW) and investment (CMA) factors to the three-factor model.","names":["Fama-French five-factor","Fama and French five-factor","Fama-French 5-factor","five-factor model","FF5"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Hodrick-Prescott filter","slug":"hodrick-prescott-filter","latex":"\\min_{\\{\\tau_t\\}} \\sum_{t=1}^{T}(y_t - \\tau_t)^2 + \\lambda \\sum_{t=2}^{T-1}\\big[(\\tau_{t+1} - \\tau_t) - (\\tau_t - \\tau_{t-1})\\big]^2","area":"Time series","about":"Separates a series into a smooth trend and a cyclical component.","names":["Hodrick-Prescott","HP filter","HP-filtered"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Newsvendor model","slug":"newsvendor-model","latex":"Q^{*} = F^{-1}\\Big(\\frac{c_u}{c_u + c_o}\\Big)","area":"Efficiency and operations","about":"Optimal stock for one selling period under uncertain demand, set by the critical ratio of underage and overage costs.","names":["newsvendor","newsboy problem","newsboy model"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Softmax function","slug":"softmax-function","latex":"\\mathrm{softmax}(z)_i = \\frac{e^{z_i}}{\\sum_{j=1}^{K} e^{z_j}}","area":"Machine learning","about":"Turns a vector of scores into probabilities.","names":["softmax"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Solow growth model","slug":"solow-growth-model","latex":"\\dot k = s\\, f(k) - (n + \\delta)\\, k","area":"Growth, trade and environment","about":"Capital per worker grows with saving and shrinks with population growth and depreciation.","names":["Solow model","Solow growth model","Solow-Swan","neoclassical growth model"],"papers":2,"papers_7d":1,"page":true},{"rank":61,"name":"Stackelberg game","slug":"stackelberg-game","latex":"\\max_{x_L}\\ \\pi_L\\big(x_L, x_F^{*}(x_L)\\big),\\quad x_F^{*}(x_L) = \\operatorname*{arg\\,max}_{x_F}\\ \\pi_F(x_L, x_F)","area":"Game theory and decision analysis","about":"A leader moves first anticipating the follower's best response; common in supply-chain models.","names":["Stackelberg"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Stochastic frontier analysis","slug":"stochastic-frontier-analysis","latex":"\\ln y_i = f(x_i; \\beta) + v_i - u_i,\\quad u_i \\ge 0","area":"Efficiency and operations","about":"Splits deviations from a production or cost frontier into noise v and inefficiency u.","names":["stochastic frontier","SFA"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Taylor rule","slug":"taylor-rule","latex":"i_t = r^{*} + \\pi_t + 0.5\\,(\\pi_t - \\pi^{*}) + 0.5\\,(y_t - \\bar y_t)","area":"Macroeconomics","about":"Sets the policy interest rate from inflation's gap to target and the output gap.","names":["Taylor rule","Taylor-type rule"],"papers":2,"papers_7d":0,"page":true},{"rank":61,"name":"Tobin's q","slug":"tobin-s-q","latex":"q = \\frac{\\text{market value of assets}}{\\text{replacement cost of assets}}","area":"Asset pricing and risk","about":"Market value of a firm relative to the replacement cost of its assets; a common proxy for firm value.","names":["Tobin's q","Tobin q"],"papers":2,"papers_7d":0,"page":true},{"rank":75,"name":"Adam optimizer","slug":"adam-optimizer","latex":"\\theta_t = \\theta_{t-1} - \\alpha\\,\\frac{\\hat m_t}{\\sqrt{\\hat v_t} + \\epsilon}","area":"Machine learning","about":"Gradient descent with running averages of the gradient (m) and its square (v).","names":["Adam optimizer","Adam optimiser","Adam optimization","Adam algorithm","AdamW"],"papers":1,"papers_7d":0,"page":true},{"rank":75,"name":"Bayes' theorem","slug":"bayes-theorem","latex":"P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}","area":"Game theory and decision analysis","about":"Updates the probability of a hypothesis A after observing evidence B.","names":["Bayes' theorem","Bayes theorem","Bayes' rule","Bayes rule","Bayesian updating"],"papers":1,"papers_7d":0,"page":true},{"rank":75,"name":"Best-worst method","slug":"best-worst-method","latex":"\\min\\ \\xi\\ \\ \\text{s.t.}\\ \\ \\lvert w_B - a_{Bj}\\, w_j \\rvert \\le \\xi,\\ \\ \\lvert w_j - a_{jW}\\, w_W \\rvert \\le \\xi,\\ \\ \\sum_j w_j = 1","area":"Game theory and decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":1,"papers_7d":0,"page":true},{"rank":75,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + 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non-causality"],"papers":8,"papers_7d":0,"page":true},{"rank":13,"name":"Herfindahl-Hirschman index","slug":"herfindahl-hirschman-index","latex":"\\mathit{HHI} = \\sum_{i=1}^{N} s_i^2","area":"Labour, inequality and competition","about":"Market concentration as the sum of squared market shares.","names":["Herfindahl","HHI"],"papers":8,"papers_7d":0,"page":true},{"rank":13,"name":"Structural equation modeling (SEM)","slug":"structural-equation-modeling-sem","latex":"\\eta = B\\eta + \\Gamma\\xi + \\zeta,\\quad y = \\Lambda_y\\,\\eta + \\varepsilon","area":"Regression models","about":"Estimates relations among latent constructs measured by several observed indicators; PLS-SEM is a common variant.","names":["structural equation model","structural equation modeling","structural equation modelling","PLS-SEM","partial least squares structural equation","CB-SEM"],"papers":8,"papers_7d":0,"page":true},{"rank":13,"name":"Total factor productivity (Solow residual)","slug":"total-factor-productivity-solow-residual","latex":"\\ln A_t = \\ln Y_t - \\alpha \\ln K_t - (1 - \\alpha) \\ln L_t","area":"Growth, trade and environment","about":"The part of output growth not explained by measured inputs.","names":["total factor productivity","Solow residual","TFP"],"papers":8,"papers_7d":1,"page":true},{"rank":18,"name":"Cointegration and error correction (VECM)","slug":"cointegration-and-error-correction-vecm","latex":"\\Delta y_t = \\Pi\\, y_{t-1} + \\sum_{i=1}^{p-1}\\Gamma_i\\,\\Delta y_{t-i} + \\varepsilon_t","area":"Time series","about":"Models series that share a long-run equilibrium; Pi holds the cointegrating relations and adjustment speeds.","names":["cointegration","co-integration","error correction model","vector error correction","VECM","Johansen test"],"papers":7,"papers_7d":0,"page":true},{"rank":18,"name":"LASSO","slug":"lasso","latex":"\\hat\\beta = \\operatorname*{arg\\,min}_{\\beta}\\ \\lVert y - X\\beta \\rVert_2^2 + \\lambda \\lVert \\beta \\rVert_1","area":"Regression models","about":"Regression with an L1 penalty that shrinks coefficients and sets many of them to exactly zero.","names":["Lasso","least absolute shrinkage"],"papers":7,"papers_7d":2,"page":true},{"rank":20,"name":"Autoregressive distributed lag (ARDL)","slug":"autoregressive-distributed-lag-ardl","latex":"y_t = \\alpha + \\sum_{i=1}^{p}\\phi_i\\, y_{t-i} + \\sum_{j=0}^{q}\\beta_j^\\top x_{t-j} + \\varepsilon_t","area":"Time series","about":"Regresses a series on its own lags and current and lagged regressors; the bounds test checks for a long-run relation.","names":["autoregressive distributed lag","ARDL","NARDL","QARDL","CS-ARDL"],"papers":6,"papers_7d":0,"page":true},{"rank":20,"name":"Markov-switching model","slug":"markov-switching-model","latex":"y_t = \\mu_{s_t} + \\varepsilon_t,\\quad \\Pr(s_t = j \\mid s_{t-1} = i) = p_{ij}","area":"Time series","about":"Lets a model's parameters change with an unobserved regime that follows a Markov chain.","names":["Markov switching","Markov regime switching","regime switching model"],"papers":6,"papers_7d":0,"page":true},{"rank":22,"name":"Spatial autoregressive models (spatial Durbin)","slug":"spatial-autoregressive-models-spatial-durbin","latex":"y = \\rho\\, W y + X\\beta + W X\\theta + \\varepsilon","area":"Regression models","about":"Lets outcomes and regressors of neighbouring units, weighted by a spatial matrix W, affect each unit.","names":["spatial Durbin","spatial autoregressive model","spatial lag model","spatial error model","spatial econometric"],"papers":5,"papers_7d":0,"page":true},{"rank":23,"name":"ARIMA","slug":"arima","latex":"\\phi(L)\\,(1 - L)^{d}\\, y_t = \\theta(L)\\,\\varepsilon_t","area":"Time series","about":"Autoregressive integrated moving-average model of a time series, with lag operator L and differencing order d.","names":["ARIMA","SARIMA","ARMA","ARFIMA","autoregressive integrated moving average","autoregressive moving average"],"papers":4,"papers_7d":0,"page":true},{"rank":23,"name":"Gradient boosting (XGBoost)","slug":"gradient-boosting-xgboost","latex":"\\mathcal{L} = \\sum_i l(y_i, \\hat y_i) + \\sum_k \\Omega(f_k),\\quad \\Omega(f) = \\gamma T + \\tfrac{1}{2}\\lambda \\lVert w \\rVert^2","area":"Machine learning","about":"Adds trees one at a time, each fitted to the errors of the ensemble so far, with a penalty on tree complexity.","names":["XGBoost","gradient boosting","LightGBM","CatBoost","GBDT"],"papers":4,"papers_7d":1,"page":true},{"rank":23,"name":"Principal component analysis (PCA)","slug":"principal-component-analysis-pca","latex":"\\max_{\\lVert w \\rVert = 1}\\ w^\\top \\Sigma\\, w","area":"Machine learning","about":"Finds the orthogonal directions of largest variance in the data.","names":["principal component analysis","principal components analysis","PCA"],"papers":4,"papers_7d":0,"page":true},{"rank":23,"name":"Random forest","slug":"random-forest","latex":"\\hat f(x) = \\frac{1}{B}\\sum_{b=1}^{B} T_b(x)","area":"Machine learning","about":"Averages many decision trees grown on bootstrap samples with random feature subsets.","names":["random forest"],"papers":4,"papers_7d":1,"page":true},{"rank":23,"name":"Sharpe ratio","slug":"sharpe-ratio","latex":"S_p = \\frac{E[R_p] - R_f}{\\sigma_p}","area":"Asset pricing and risk","about":"Excess return of a portfolio per unit of total risk.","names":["Sharpe ratio"],"papers":4,"papers_7d":1,"page":true},{"rank":23,"name":"Value at risk (VaR)","slug":"value-at-risk-var","latex":"\\mathrm{VaR}_\\alpha(L) = \\inf\\{\\ell \\in \\mathbb{R} : \\Pr(L > \\ell) \\le 1 - \\alpha\\}","area":"Asset pricing and risk","about":"The loss that is exceeded with probability at most 1 - alpha over a given horizon.","names":["value at risk","VaR"],"papers":4,"papers_7d":1,"page":true},{"rank":29,"name":"Expected shortfall (CVaR)","slug":"expected-shortfall-cvar","latex":"\\mathrm{ES}_\\alpha(L) = \\frac{1}{1 - \\alpha}\\int_\\alpha^{1} \\mathrm{VaR}_u(L)\\,du","area":"Asset pricing and risk","about":"Average loss in the worst 1 - alpha share of outcomes; also called conditional value at risk.","names":["expected shortfall","conditional value at risk","CVaR"],"papers":3,"papers_7d":0,"page":true},{"rank":29,"name":"Gini coefficient","slug":"gini-coefficient","latex":"G = \\frac{\\sum_{i=1}^{n}\\sum_{j=1}^{n} \\lvert x_i - x_j \\rvert}{2 n^2 \\bar x}","area":"Labour, inequality and competition","about":"Inequality measure from 0 (equal) to 1 (one unit has everything).","names":["Gini coefficient","Gini index"],"papers":3,"papers_7d":0,"page":true},{"rank":31,"name":"Amihud illiquidity ratio","slug":"amihud-illiquidity-ratio","latex":"\\mathit{ILLIQ}_i = \\frac{1}{D_i}\\sum_{d=1}^{D_i}\\frac{\\lvert R_{id} \\rvert}{\\mathit{DVOL}_{id}}","area":"Asset pricing and risk","about":"Average absolute daily return per dollar of trading volume: the price impact of trading.","names":["Amihud illiquidity","Amihud's illiquidity","Amihud measure","Amihud's measure","Amihud ratio"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Capital asset pricing model (CAPM)","slug":"capital-asset-pricing-model-capm","latex":"E[R_i] = R_f + \\beta_i\\,(E[R_m] - R_f)","area":"Asset pricing and risk","about":"Expected return of an asset as the risk-free rate plus its market beta times the market risk premium.","names":["capital asset pricing model","CAPM"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Fama-French five-factor model","slug":"fama-french-five-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + r_i\\,\\mathit{RMW}_t + c_i\\,\\mathit{CMA}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds profitability (RMW) and investment (CMA) factors to the three-factor model.","names":["Fama-French five-factor","Fama and French five-factor","Fama-French 5-factor","five-factor model","FF5"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Heckman selection model","slug":"heckman-selection-model","latex":"E[y_i \\mid x_i, s_i = 1] = x_i^\\top\\beta + \\rho\\,\\sigma_\\varepsilon\\,\\lambda(z_i^\\top\\gamma),\\quad \\lambda(\\cdot) = \\frac{\\phi(\\cdot)}{\\Phi(\\cdot)}","area":"Causal inference","about":"Corrects for non-random selection of the observed sample with the inverse Mills ratio from a first-stage probit.","names":["Heckman selection","Heckman two-step","Heckman two-stage","Heckman correction","Heckman model","inverse Mills ratio","sample selection model"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Kalman filter","slug":"kalman-filter","latex":"\\hat x_{t \\mid t} = \\hat x_{t \\mid t-1} + K_t\\,(y_t - H\\,\\hat x_{t \\mid t-1})","area":"Time series","about":"Recursively updates estimates of an unobserved state from noisy observations.","names":["Kalman filter","Kalman filtering","Kalman smoother"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Shapley value (SHAP)","slug":"shapley-value-shap","latex":"\\phi_i(v) = \\sum_{S \\subseteq N \\setminus \\{i\\}} \\frac{\\lvert S \\rvert!\\,(n - \\lvert S \\rvert - 1)!}{n!}\\big[v(S \\cup \\{i\\}) - v(S)\\big]","area":"Game theory and decision analysis","about":"A player's average marginal contribution over all coalitions; SHAP uses it to explain machine-learning predictions.","names":["Shapley value","SHAP","Shapley additive explanation"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Synthetic control method","slug":"synthetic-control-method","latex":"\\hat Y^{N}_{1t} = \\sum_{j=2}^{J+1} w_j^{*}\\, Y_{jt},\\quad w_j^{*} \\ge 0,\\ \\sum_j w_j^{*} = 1","area":"Causal inference","about":"Builds the counterfactual for a treated unit as a weighted average of untreated units.","names":["synthetic control"],"papers":2,"papers_7d":0,"page":true},{"rank":31,"name":"Tobin's q","slug":"tobin-s-q","latex":"q = \\frac{\\text{market value of assets}}{\\text{replacement cost of assets}}","area":"Asset pricing and risk","about":"Market value of a firm relative to the replacement cost of its assets; a common proxy for firm value.","names":["Tobin's q","Tobin q"],"papers":2,"papers_7d":0,"page":true},{"rank":39,"name":"Bayes' theorem","slug":"bayes-theorem","latex":"P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}","area":"Game theory and decision analysis","about":"Updates the probability of a hypothesis A after observing evidence B.","names":["Bayes' theorem","Bayes theorem","Bayes' rule","Bayes rule","Bayesian updating"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Bellman equation","slug":"bellman-equation","latex":"V(s) = \\max_{a}\\left\\{ r(s, a) + \\beta \\sum_{s'} P(s' \\mid s, a)\\, V(s') \\right\\}","area":"Game theory and decision analysis","about":"Recursive condition for the value of a dynamic optimization or Markov decision problem.","names":["Bellman equation","Hamilton-Jacobi-Bellman","HJB equation","Bellman optimality"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Carhart four-factor model","slug":"carhart-four-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + m_i\\,\\mathit{UMD}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds a momentum factor (UMD) to the Fama-French three factors; widely used for fund performance.","names":["Carhart four-factor","Carhart 4-factor","Carhart model","four-factor model"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Convolutional neural network (CNN)","slug":"convolutional-neural-network-cnn","latex":"(I * K)(i, j) = \\sum_{m}\\sum_{n} I(i + m,\\, j + n)\\, K(m, n)","area":"Machine learning","about":"Networks built from learned convolution filters, standard for images and other grid data.","names":["convolutional neural network","CNN","ConvNet"],"papers":1,"papers_7d":1,"page":true},{"rank":39,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + U_2},\\quad T = \\alpha U_1 + \\beta U_2,\\quad D = \\sqrt{C\\, T}","area":"Game theory and decision analysis","about":"Measures how well two systems (for example the economy and the environment) develop together.","names":["coupling coordination","coupled coordination"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"CoVaR (systemic risk)","slug":"covar-systemic-risk","latex":"\\Pr\\big(X^{\\mathrm{sys}} \\le \\mathrm{CoVaR}_q^{\\mathrm{sys} \\mid i} \\mid X^{i} = \\mathrm{VaR}_q^{i}\\big) = q","area":"Asset pricing and risk","about":"Value at risk of the financial system conditional on an institution being in distress; Delta CoVaR measures its contribution.","names":["CoVaR","delta CoVaR"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Cox proportional hazards model","slug":"cox-proportional-hazards-model","latex":"h(t \\mid x) = h_0(t)\\,\\exp(x^\\top\\beta)","area":"Regression models","about":"Models the hazard of an event over time as a baseline hazard scaled by the regressors.","names":["Cox proportional hazard","proportional hazards model","Cox regression","Cox model","Cox hazard model"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Data envelopment analysis (DEA)","slug":"data-envelopment-analysis-dea","latex":"\\max_{u, v}\\ \\frac{\\sum_r u_r\\, y_{r0}}{\\sum_i v_i\\, x_{i0}}\\ \\ \\text{s.t.}\\ \\ \\frac{\\sum_r u_r\\, y_{rj}}{\\sum_i v_i\\, x_{ij}} \\le 1\\ \\ \\forall j","area":"Efficiency and operations","about":"Scores the efficiency of each unit as its best ratio of weighted outputs to weighted inputs relative to all units.","names":["data envelopment analysis","DEA model","super-efficiency DEA","slacks-based measure","SBM model","network DEA","DEA"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Dechow-Dichev accruals quality","slug":"dechow-dichev-accruals-quality","latex":"\\Delta WC_{it} = \\beta_0 + \\beta_1\\, CFO_{i,t-1} + \\beta_2\\, CFO_{it} + \\beta_3\\, CFO_{i,t+1} + \\varepsilon_{it}","area":"Accounting","about":"Measures how well working-capital accruals map into past, current and future cash flows.","names":["Dechow and Dichev","Dechow-Dichev","accruals quality","accrual quality"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Generative adversarial network (GAN)","slug":"generative-adversarial-network-gan","latex":"\\min_G \\max_D\\ E_x\\big[\\log D(x)\\big] + E_z\\big[\\log\\big(1 - D(G(z))\\big)\\big]","area":"Machine learning","about":"A generator and a discriminator trained against each other.","names":["generative adversarial","GAN"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Graph neural network (graph convolution)","slug":"graph-neural-network-graph-convolution","latex":"H^{(l+1)} = \\sigma\\big(\\tilde D^{-1/2} \\tilde A\\, \\tilde D^{-1/2} H^{(l)} W^{(l)}\\big)","area":"Machine learning","about":"Updates each node's representation from its neighbours' representations.","names":["graph neural network","graph convolutional network","graph convolution","graph attention network","GCN","GNN"],"papers":1,"papers_7d":1,"page":true},{"rank":39,"name":"Hodrick-Prescott filter","slug":"hodrick-prescott-filter","latex":"\\min_{\\{\\tau_t\\}} \\sum_{t=1}^{T}(y_t - \\tau_t)^2 + \\lambda \\sum_{t=2}^{T-1}\\big[(\\tau_{t+1} - \\tau_t) - (\\tau_t - \\tau_{t-1})\\big]^2","area":"Time series","about":"Separates a series into a smooth trend and a cyclical component.","names":["Hodrick-Prescott","HP filter","HP-filtered"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Lerner index","slug":"lerner-index","latex":"L = \\frac{P - MC}{P}","area":"Labour, inequality and competition","about":"Market power as the markup of price over marginal cost.","names":["Lerner index"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Long short-term memory (LSTM)","slug":"long-short-term-memory-lstm","latex":"c_t = f_t \\odot c_{t-1} + i_t \\odot \\tilde c_t,\\quad h_t = o_t \\odot \\tanh(c_t)","area":"Machine learning","about":"Recurrent network cell whose gates decide what to keep, add and output at each step.","names":["LSTM","long short-term memory","BiLSTM","Bi-LSTM"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Mean-variance portfolio (Markowitz)","slug":"mean-variance-portfolio-markowitz","latex":"\\min_{w}\\ w^\\top \\Sigma\\, w\\ \\ \\text{s.t.}\\ \\ w^\\top \\mu = \\mu_p,\\ \\ w^\\top \\mathbf{1} = 1","area":"Asset pricing and risk","about":"Chooses portfolio weights with the lowest variance for a target expected return.","names":["mean-variance","Markowitz","modern portfolio theory"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Nash equilibrium","slug":"nash-equilibrium","latex":"u_i(s_i^{*}, s_{-i}^{*}) \\ge u_i(s_i, s_{-i}^{*})\\quad \\forall i,\\ \\forall s_i","area":"Game theory and decision analysis","about":"No player can gain by changing strategy alone.","names":["Nash equilibrium","Nash equilibria"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"New Keynesian Phillips curve","slug":"new-keynesian-phillips-curve","latex":"\\pi_t = \\beta\\,E_t[\\pi_{t+1}] + \\kappa\\, x_t","area":"Macroeconomics","about":"Links inflation to expected future inflation and the output gap (or real marginal cost) x.","names":["Phillips curve"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"TOPSIS","slug":"topsis","latex":"C_i = \\frac{d_i^{-}}{d_i^{+} + d_i^{-}}","area":"Game theory and decision analysis","about":"Ranks alternatives by closeness to the ideal solution and distance from the worst one.","names":["TOPSIS"],"papers":1,"papers_7d":0,"page":true},{"rank":39,"name":"Variational autoencoder (ELBO)","slug":"variational-autoencoder-elbo","latex":"\\log p_\\theta(x) \\ge E_{q_\\phi(z \\mid x)}\\big[\\log p_\\theta(x \\mid z)\\big] - D_{\\mathrm{KL}}\\big(q_\\phi(z \\mid x) \\parallel p(z)\\big)","area":"Machine learning","about":"Generative model trained by maximizing the evidence lower bound on the data likelihood.","names":["variational autoencoder","variational auto-encoder","evidence lower bound","ELBO","VAE"],"papers":1,"papers_7d":0,"page":true},{"rank":58,"name":"Adam optimizer","slug":"adam-optimizer","latex":"\\theta_t = \\theta_{t-1} - \\alpha\\,\\frac{\\hat m_t}{\\sqrt{\\hat v_t} + \\epsilon}","area":"Machine learning","about":"Gradient descent with running averages of the gradient (m) and its square (v).","names":["Adam optimizer","Adam optimiser","Adam optimization","Adam algorithm","AdamW"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Altman Z-score","slug":"altman-z-score","latex":"Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5","area":"Asset pricing and risk","about":"Bankruptcy predictor that weights five accounting ratios (working capital, retained earnings, EBIT, market equity, sales).","names":["Altman Z","Altman's Z"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Analytic hierarchy process (AHP)","slug":"analytic-hierarchy-process-ahp","latex":"A\\, w = \\lambda_{\\max}\\, w,\\quad CR = \\frac{(\\lambda_{\\max} - n)/(n - 1)}{RI}","area":"Game theory and decision analysis","about":"Derives criteria weights from pairwise comparisons; CR checks their consistency.","names":["analytic hierarchy process","analytical hierarchy process","AHP"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Bass diffusion model","slug":"bass-diffusion-model","latex":"\\frac{f(t)}{1 - F(t)} = p + q\\, F(t)","area":"Efficiency and operations","about":"Adoption of a new product driven by innovation (p) and imitation (q).","names":["Bass diffusion","Bass model"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Basu asymmetric timeliness","slug":"basu-asymmetric-timeliness","latex":"\\frac{EPS_{it}}{P_{i,t-1}} = \\beta_0 + \\beta_1 D_{it} + \\beta_2 R_{it} + \\beta_3 D_{it} R_{it} + \\varepsilon_{it}","area":"Accounting","about":"Measures accounting conservatism as how much faster earnings reflect bad news (negative returns) than good news.","names":["asymmetric timeliness","Basu model","Basu (1997)","Basu's model"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Beneish M-score","slug":"beneish-m-score","latex":"M = -4.84 + 0.92\\,\\mathit{DSRI} + 0.528\\,\\mathit{GMI} + 0.404\\,\\mathit{AQI} + 0.892\\,\\mathit{SGI} + 0.115\\,\\mathit{DEPI} - 0.172\\,\\mathit{SGAI} + 4.679\\,\\mathit{TATA} - 0.327\\,\\mathit{LVGI}","area":"Accounting","about":"Flags likely earnings manipulation from eight financial-statement ratios.","names":["Beneish M-score","Beneish model","Beneish's M-score","M-score"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Best-worst method","slug":"best-worst-method","latex":"\\min\\ \\xi\\ \\ \\text{s.t.}\\ \\ \\lvert w_B - a_{Bj}\\, w_j \\rvert \\le \\xi,\\ \\ \\lvert w_j - a_{jW}\\, w_W \\rvert \\le \\xi,\\ \\ \\sum_j w_j = 1","area":"Game theory and decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"Black-Scholes formula","slug":"black-scholes-formula","latex":"C = S_0\\,N(d_1) - K e^{-rT} N(d_2),\\quad d_{1,2} = \\frac{\\ln(S_0/K) + (r \\pm \\sigma^2/2)\\,T}{\\sigma\\sqrt{T}}","area":"Asset pricing and risk","about":"Price of a European call option on a stock with constant volatility and interest rate.","names":["Black-Scholes","Black and Scholes"],"papers":0,"papers_7d":0,"page":false},{"rank":58,"name":"CES production 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modelling","PLS-SEM","partial least squares structural equation","CB-SEM"],"papers":3,"papers_7d":0,"page":true},{"rank":5,"name":"Mediation model (indirect effect)","slug":"mediation-model-indirect-effect","latex":"M = \\alpha_0 + a X + e_1,\\quad Y = \\beta_0 + c' X + b M + e_2,\\quad \\text{indirect effect} = a\\,b","area":"Causal inference","about":"Splits the effect of X on Y into a direct part and a part that runs through a mediator M.","names":["mediation analysis","mediating effect","mediation effect","mediation model","Sobel test","Baron and Kenny"],"papers":2,"papers_7d":0,"page":true},{"rank":5,"name":"Probit model","slug":"probit-model","latex":"\\Pr(y = 1 \\mid x) = \\Phi(x^\\top\\beta)","area":"Regression models","about":"Models the probability of a binary outcome with the standard normal distribution function.","names":["probit"],"papers":2,"papers_7d":0,"page":true},{"rank":5,"name":"Propensity score matching","slug":"propensity-score-matching","latex":"e(x) = \\Pr(D = 1 \\mid X = x)","area":"Causal inference","about":"Matches treated and untreated units with similar probabilities of treatment given their characteristics.","names":["propensity score","PSM"],"papers":2,"papers_7d":0,"page":true},{"rank":5,"name":"Quantile regression","slug":"quantile-regression","latex":"\\hat\\beta_\\tau = \\operatorname*{arg\\,min}_{\\beta} \\sum_{i} \\rho_\\tau(y_i - x_i^\\top\\beta),\\quad \\rho_\\tau(u) = u\\,(\\tau - \\mathbf{1}\\{u < 0\\})","area":"Regression models","about":"Estimates how regressors shift a chosen quantile of the outcome rather than its mean.","names":["quantile regression","quantile-on-quantile"],"papers":2,"papers_7d":0,"page":true},{"rank":9,"name":"ARIMA","slug":"arima","latex":"\\phi(L)\\,(1 - L)^{d}\\, y_t = \\theta(L)\\,\\varepsilon_t","area":"Time series","about":"Autoregressive integrated moving-average model of a time series, with lag operator L and differencing order d.","names":["ARIMA","SARIMA","ARMA","ARFIMA","autoregressive integrated moving average","autoregressive moving average"],"papers":1,"papers_7d":0,"page":true},{"rank":9,"name":"Cox proportional hazards model","slug":"cox-proportional-hazards-model","latex":"h(t \\mid x) = h_0(t)\\,\\exp(x^\\top\\beta)","area":"Regression models","about":"Models the hazard of an event over time as a baseline hazard scaled by the regressors.","names":["Cox proportional hazard","proportional hazards model","Cox regression","Cox model","Cox hazard model"],"papers":1,"papers_7d":0,"page":true},{"rank":9,"name":"Dechow-Dichev accruals quality","slug":"dechow-dichev-accruals-quality","latex":"\\Delta WC_{it} = \\beta_0 + \\beta_1\\, CFO_{i,t-1} + \\beta_2\\, CFO_{it} + \\beta_3\\, CFO_{i,t+1} + \\varepsilon_{it}","area":"Accounting","about":"Measures how well working-capital accruals map into past, current and future cash flows.","names":["Dechow and Dichev","Dechow-Dichev","accruals quality","accrual quality"],"papers":1,"papers_7d":1,"page":true},{"rank":9,"name":"Event study (abnormal returns)","slug":"event-study-abnormal-returns","latex":"AR_{it} = R_{it} - (\\hat\\alpha_i + \\hat\\beta_i R_{mt}),\\quad CAR_i = \\sum_{t=t_1}^{t_2} AR_{it}","area":"Causal inference","about":"Measures returns beyond what a market model predicts around an event such as an announcement.","names":["abnormal return","cumulative abnormal return","buy-and-hold abnormal return"],"papers":1,"papers_7d":0,"page":true},{"rank":9,"name":"Generalized method of moments (GMM)","slug":"generalized-method-of-moments-gmm","latex":"\\hat\\theta = \\operatorname*{arg\\,min}_{\\theta}\\ \\bar g(\\theta)^\\top W\\, \\bar g(\\theta),\\quad \\bar g(\\theta) = \\frac{1}{n}\\sum_{i=1}^{n} g(w_i, \\theta)","area":"Regression models","about":"Estimates parameters by making sample moment conditions as close to zero as possible; system and difference GMM are common in dynamic panels.","names":["generalized method of moments","generalised method of moments","system GMM","difference GMM","GMM estimator","GMM estimation","two-step GMM","Arellano-Bond"],"papers":1,"papers_7d":0,"page":true},{"rank":9,"name":"Logistic regression (logit)","slug":"logistic-regression-logit","latex":"\\Pr(y = 1 \\mid x) = \\frac{1}{1 + e^{-x^\\top\\beta}}","area":"Regression models","about":"Models the probability of a binary outcome with the logistic function.","names":["logistic regression","logit"],"papers":1,"papers_7d":0,"page":true},{"rank":9,"name":"Regression discontinuity design","slug":"regression-discontinuity-design","latex":"\\tau = \\lim_{x \\downarrow c} E[Y \\mid X = x] - \\lim_{x \\uparrow c} E[Y \\mid X = x]","area":"Causal inference","about":"Estimates an effect from the jump in outcomes at a cutoff c of a running variable X that decides treatment.","names":["regression discontinuity","RDD"],"papers":1,"papers_7d":0,"page":true},{"rank":9,"name":"Synthetic control method","slug":"synthetic-control-method","latex":"\\hat Y^{N}_{1t} = \\sum_{j=2}^{J+1} w_j^{*}\\, Y_{jt},\\quad w_j^{*} \\ge 0,\\ \\sum_j w_j^{*} = 1","area":"Causal inference","about":"Builds the counterfactual for a treated unit as a weighted average of untreated units.","names":["synthetic control"],"papers":1,"papers_7d":0,"page":true},{"rank":17,"name":"Adam optimizer","slug":"adam-optimizer","latex":"\\theta_t = \\theta_{t-1} - \\alpha\\,\\frac{\\hat m_t}{\\sqrt{\\hat v_t} + \\epsilon}","area":"Machine learning","about":"Gradient descent with running averages of the gradient (m) and its square (v).","names":["Adam optimizer","Adam optimiser","Adam optimization","Adam algorithm","AdamW"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Altman Z-score","slug":"altman-z-score","latex":"Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5","area":"Asset pricing and risk","about":"Bankruptcy predictor that weights five accounting ratios (working capital, retained earnings, EBIT, market equity, sales).","names":["Altman Z","Altman's Z"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Amihud illiquidity ratio","slug":"amihud-illiquidity-ratio","latex":"\\mathit{ILLIQ}_i = \\frac{1}{D_i}\\sum_{d=1}^{D_i}\\frac{\\lvert R_{id} \\rvert}{\\mathit{DVOL}_{id}}","area":"Asset pricing and risk","about":"Average absolute daily return per dollar of trading volume: the price impact of trading.","names":["Amihud illiquidity","Amihud's illiquidity","Amihud measure","Amihud's measure","Amihud ratio"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Analytic hierarchy process (AHP)","slug":"analytic-hierarchy-process-ahp","latex":"A\\, w = \\lambda_{\\max}\\, w,\\quad CR = \\frac{(\\lambda_{\\max} - n)/(n - 1)}{RI}","area":"Game theory and decision analysis","about":"Derives criteria weights from pairwise comparisons; CR checks their consistency.","names":["analytic hierarchy process","analytical hierarchy process","AHP"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Autoregressive distributed lag (ARDL)","slug":"autoregressive-distributed-lag-ardl","latex":"y_t = \\alpha + \\sum_{i=1}^{p}\\phi_i\\, y_{t-i} + \\sum_{j=0}^{q}\\beta_j^\\top x_{t-j} + \\varepsilon_t","area":"Time series","about":"Regresses a series on its own lags and current and lagged regressors; the bounds test checks for a long-run relation.","names":["autoregressive distributed lag","ARDL","NARDL","QARDL","CS-ARDL"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Bass diffusion model","slug":"bass-diffusion-model","latex":"\\frac{f(t)}{1 - F(t)} = p + q\\, F(t)","area":"Efficiency and operations","about":"Adoption of a new product driven by innovation (p) and imitation (q).","names":["Bass diffusion","Bass model"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Basu asymmetric timeliness","slug":"basu-asymmetric-timeliness","latex":"\\frac{EPS_{it}}{P_{i,t-1}} = \\beta_0 + \\beta_1 D_{it} + \\beta_2 R_{it} + \\beta_3 D_{it} R_{it} + \\varepsilon_{it}","area":"Accounting","about":"Measures accounting conservatism as how much faster earnings reflect bad news (negative returns) than good news.","names":["asymmetric timeliness","Basu model","Basu (1997)","Basu's model"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Bayes' theorem","slug":"bayes-theorem","latex":"P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}","area":"Game theory and decision analysis","about":"Updates the probability of a hypothesis A after observing evidence B.","names":["Bayes' theorem","Bayes theorem","Bayes' rule","Bayes rule","Bayesian updating"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Bellman equation","slug":"bellman-equation","latex":"V(s) = \\max_{a}\\left\\{ r(s, a) + \\beta \\sum_{s'} P(s' \\mid s, a)\\, V(s') \\right\\}","area":"Game theory and decision analysis","about":"Recursive condition for the value of a dynamic optimization or Markov decision problem.","names":["Bellman equation","Hamilton-Jacobi-Bellman","HJB equation","Bellman optimality"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Beneish M-score","slug":"beneish-m-score","latex":"M = -4.84 + 0.92\\,\\mathit{DSRI} + 0.528\\,\\mathit{GMI} + 0.404\\,\\mathit{AQI} + 0.892\\,\\mathit{SGI} + 0.115\\,\\mathit{DEPI} - 0.172\\,\\mathit{SGAI} + 4.679\\,\\mathit{TATA} - 0.327\\,\\mathit{LVGI}","area":"Accounting","about":"Flags likely earnings manipulation from eight financial-statement ratios.","names":["Beneish M-score","Beneish model","Beneish's M-score","M-score"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Best-worst method","slug":"best-worst-method","latex":"\\min\\ \\xi\\ \\ \\text{s.t.}\\ \\ \\lvert w_B - a_{Bj}\\, w_j \\rvert \\le \\xi,\\ \\ \\lvert w_j - a_{jW}\\, w_W \\rvert \\le \\xi,\\ \\ \\sum_j w_j = 1","area":"Game theory and decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Black-Scholes formula","slug":"black-scholes-formula","latex":"C = S_0\\,N(d_1) - K e^{-rT} N(d_2),\\quad d_{1,2} = \\frac{\\ln(S_0/K) + (r \\pm \\sigma^2/2)\\,T}{\\sigma\\sqrt{T}}","area":"Asset pricing and risk","about":"Price of a European call option on a stock with constant volatility and interest rate.","names":["Black-Scholes","Black and Scholes"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Capital asset pricing model (CAPM)","slug":"capital-asset-pricing-model-capm","latex":"E[R_i] = R_f + \\beta_i\\,(E[R_m] - R_f)","area":"Asset pricing and risk","about":"Expected return of an asset as the risk-free rate plus its market beta times the market risk premium.","names":["capital asset pricing model","CAPM"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Carhart four-factor model","slug":"carhart-four-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + m_i\\,\\mathit{UMD}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds a momentum factor (UMD) to the Fama-French three factors; widely used for fund performance.","names":["Carhart four-factor","Carhart 4-factor","Carhart model","four-factor model"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"CES production function","slug":"ces-production-function","latex":"Y = A\\big[\\alpha K^{\\rho} + (1 - \\alpha) L^{\\rho}\\big]^{1/\\rho}","area":"Growth, trade and environment","about":"Production (or utility) with a constant elasticity of substitution 1/(1 - rho) between inputs.","names":["constant elasticity of substitution","CES production","CES utility","CES function"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Cobb-Douglas production function","slug":"cobb-douglas-production-function","latex":"Y = A\\, K^{\\alpha} L^{1 - \\alpha}","area":"Growth, trade and environment","about":"Output from capital and labour with constant output shares.","names":["Cobb-Douglas"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Cointegration and error correction (VECM)","slug":"cointegration-and-error-correction-vecm","latex":"\\Delta y_t = \\Pi\\, y_{t-1} + \\sum_{i=1}^{p-1}\\Gamma_i\\,\\Delta y_{t-i} + \\varepsilon_t","area":"Time series","about":"Models series that share a long-run equilibrium; Pi holds the cointegrating relations and adjustment speeds.","names":["cointegration","co-integration","error correction model","vector error correction","VECM","Johansen test"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Consumption Euler equation","slug":"consumption-euler-equation","latex":"u'(c_t) = \\beta\\,E_t\\big[(1 + r_{t+1})\\,u'(c_{t+1})\\big]","area":"Macroeconomics","about":"Optimal saving condition: the marginal utility of consuming today equals the discounted expected return of saving it.","names":["Euler equation","consumption Euler"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Contrastive loss (InfoNCE)","slug":"contrastive-loss-infonce","latex":"\\mathcal{L} = -\\log \\frac{\\exp(\\mathrm{sim}(z_i, z_j)/\\tau)}{\\sum_{k \\ne i} \\exp(\\mathrm{sim}(z_i, z_k)/\\tau)}","area":"Machine learning","about":"Pulls representations of matching pairs together and pushes others apart.","names":["InfoNCE","contrastive loss","contrastive learning","NT-Xent"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Convolutional neural network (CNN)","slug":"convolutional-neural-network-cnn","latex":"(I * K)(i, j) = \\sum_{m}\\sum_{n} I(i + m,\\, j + n)\\, K(m, n)","area":"Machine learning","about":"Networks built from learned convolution filters, standard for images and other grid data.","names":["convolutional neural network","CNN","ConvNet"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + U_2},\\quad T = \\alpha U_1 + \\beta U_2,\\quad D = \\sqrt{C\\, T}","area":"Game theory and decision analysis","about":"Measures how well two systems (for example the economy and the environment) develop together.","names":["coupling coordination","coupled coordination"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"CoVaR (systemic risk)","slug":"covar-systemic-risk","latex":"\\Pr\\big(X^{\\mathrm{sys}} \\le \\mathrm{CoVaR}_q^{\\mathrm{sys} \\mid i} \\mid X^{i} = \\mathrm{VaR}_q^{i}\\big) = q","area":"Asset pricing and risk","about":"Value at risk of the financial system conditional on an institution being in distress; Delta CoVaR measures its contribution.","names":["CoVaR","delta CoVaR"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Covered interest parity","slug":"covered-interest-parity","latex":"\\frac{F_t}{S_t} = \\frac{1 + i_t}{1 + i_t^{*}}","area":"Macroeconomics","about":"The forward premium of a currency equals the interest rate differential; deviations signal funding frictions.","names":["covered interest parity","covered interest rate parity","CIP deviation"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Cross-entropy loss","slug":"cross-entropy-loss","latex":"\\mathcal{L} = -\\sum_{c=1}^{C} y_c \\log \\hat y_c","area":"Machine learning","about":"Standard loss for classification: the negative log-probability of the true class.","names":["cross-entropy"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Data envelopment analysis (DEA)","slug":"data-envelopment-analysis-dea","latex":"\\max_{u, v}\\ \\frac{\\sum_r u_r\\, y_{r0}}{\\sum_i v_i\\, x_{i0}}\\ \\ \\text{s.t.}\\ \\ \\frac{\\sum_r u_r\\, y_{rj}}{\\sum_i v_i\\, x_{ij}} \\le 1\\ \\ \\forall j","area":"Efficiency and operations","about":"Scores the efficiency of each unit as its best ratio of weighted outputs to weighted inputs relative to all units.","names":["data envelopment analysis","DEA model","super-efficiency DEA","slacks-based measure","SBM model","network DEA","DEA"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"DEMATEL","slug":"dematel","latex":"T = X\\,(I - X)^{-1}","area":"Game theory and decision analysis","about":"Maps cause-and-effect relations among factors from a normalized direct-influence matrix X.","names":["DEMATEL"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Denoising diffusion model","slug":"denoising-diffusion-model","latex":"\\mathcal{L} = E_{t, x_0, \\epsilon}\\Big[\\left\\lVert \\epsilon - \\epsilon_\\theta\\big(\\sqrt{\\bar\\alpha_t}\\, x_0 + \\sqrt{1 - \\bar\\alpha_t}\\, \\epsilon,\\ t\\big) \\right\\rVert^2\\Big]","area":"Machine learning","about":"Generative model that learns to remove noise step by step; the basis of current image generators.","names":["denoising diffusion","diffusion probabilistic","latent diffusion","score-based generative","Stable Diffusion"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Dividend discount (Gordon growth) model","slug":"dividend-discount-gordon-growth-model","latex":"P_0 = \\frac{D_1}{r - g}","area":"Asset pricing and risk","about":"Values a stock as next year's dividend divided by the discount rate minus the dividend growth rate.","names":["dividend discount model","Gordon growth model"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Economic order quantity (EOQ)","slug":"economic-order-quantity-eoq","latex":"Q^{*} = \\sqrt{\\frac{2 D S}{H}}","area":"Efficiency and operations","about":"Order size that minimizes ordering plus holding costs.","names":["economic order quantity","EOQ"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Entropy weight method","slug":"entropy-weight-method","latex":"e_j = -\\frac{1}{\\ln n}\\sum_{i=1}^{n} p_{ij}\\ln p_{ij},\\quad w_j = \\frac{1 - e_j}{\\sum_k (1 - e_k)}","area":"Game theory and decision analysis","about":"Weights indicators by how much their values vary across units, often to build composite indices.","names":["entropy weight","entropy weighting","entropy method"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Environmental Kuznets curve","slug":"environmental-kuznets-curve","latex":"\\ln E_{it} = \\beta_0 + \\beta_1 \\ln Y_{it} + \\beta_2 (\\ln Y_{it})^2 + \\varepsilon_{it}","area":"Growth, trade and environment","about":"Tests whether pollution first rises and then falls as income grows (beta_2 < 0).","names":["environmental Kuznets curve","Kuznets curve","EKC"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Expected shortfall (CVaR)","slug":"expected-shortfall-cvar","latex":"\\mathrm{ES}_\\alpha(L) = \\frac{1}{1 - \\alpha}\\int_\\alpha^{1} \\mathrm{VaR}_u(L)\\,du","area":"Asset pricing and risk","about":"Average loss in the worst 1 - alpha share of outcomes; also called conditional value at risk.","names":["expected shortfall","conditional value at risk","CVaR"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Fama-French five-factor model","slug":"fama-french-five-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + r_i\\,\\mathit{RMW}_t + c_i\\,\\mathit{CMA}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds profitability (RMW) and investment (CMA) factors to the three-factor model.","names":["Fama-French five-factor","Fama and French five-factor","Fama-French 5-factor","five-factor model","FF5"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Fama-French three-factor model","slug":"fama-french-three-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Explains excess returns with the market, size (SMB) and value (HML) factors.","names":["Fama-French three-factor","Fama and French three-factor","Fama-French 3-factor","Fama and French 3-factor","three-factor model","FF3"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Fisher equation","slug":"fisher-equation","latex":"i_t \\approx r_t + E_t[\\pi_{t+1}]","area":"Macroeconomics","about":"The nominal interest rate equals the real rate plus expected inflation.","names":["Fisher equation","Fisher effect","Fisher hypothesis"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"GARCH","slug":"garch","latex":"\\sigma_t^2 = \\omega + \\alpha\\,\\varepsilon_{t-1}^2 + \\beta\\,\\sigma_{t-1}^2","area":"Time series","about":"Models time-varying volatility: today's variance depends on yesterday's shock and variance (GARCH(1,1)).","names":["GARCH","EGARCH","TGARCH","FIGARCH","MGARCH","generalized autoregressive conditional heteroskedasticity","generalized autoregressive conditional heteroscedasticity"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Gated recurrent unit (GRU)","slug":"gated-recurrent-unit-gru","latex":"h_t = (1 - z_t) \\odot h_{t-1} + z_t \\odot \\tilde h_t","area":"Machine learning","about":"A simpler gated recurrent cell with update and reset gates.","names":["gated recurrent unit","GRU"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Generative adversarial network (GAN)","slug":"generative-adversarial-network-gan","latex":"\\min_G \\max_D\\ E_x\\big[\\log D(x)\\big] + E_z\\big[\\log\\big(1 - D(G(z))\\big)\\big]","area":"Machine learning","about":"A generator and a discriminator trained against each other.","names":["generative adversarial","GAN"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Gini coefficient","slug":"gini-coefficient","latex":"G = \\frac{\\sum_{i=1}^{n}\\sum_{j=1}^{n} \\lvert x_i - x_j \\rvert}{2 n^2 \\bar x}","area":"Labour, inequality and competition","about":"Inequality measure from 0 (equal) to 1 (one unit has everything).","names":["Gini coefficient","Gini index"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Gradient boosting (XGBoost)","slug":"gradient-boosting-xgboost","latex":"\\mathcal{L} = \\sum_i l(y_i, \\hat y_i) + \\sum_k \\Omega(f_k),\\quad \\Omega(f) = \\gamma T + \\tfrac{1}{2}\\lambda \\lVert w \\rVert^2","area":"Machine learning","about":"Adds trees one at a time, each fitted to the errors of the ensemble so far, with a penalty on tree complexity.","names":["XGBoost","gradient boosting","LightGBM","CatBoost","GBDT"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Gradient descent","slug":"gradient-descent","latex":"\\theta_{t+1} = \\theta_t - \\eta\\, \\nabla_\\theta \\mathcal{L}(\\theta_t)","area":"Machine learning","about":"Moves parameters a step against the gradient of the loss; stochastic gradient descent uses mini-batches.","names":["gradient descent","SGD"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Granger causality","slug":"granger-causality","latex":"y_t = \\sum_{i=1}^{p} a_i\\, y_{t-i} + \\sum_{j=1}^{p} b_j\\, x_{t-j} + \\varepsilon_t,\\quad H_0: b_1 = \\dots = b_p = 0","area":"Time series","about":"Tests whether past values of x help predict y beyond y's own past.","names":["Granger causality","Granger cause","Granger causal","Granger non-causality"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Graph neural network (graph convolution)","slug":"graph-neural-network-graph-convolution","latex":"H^{(l+1)} = \\sigma\\big(\\tilde D^{-1/2} \\tilde A\\, \\tilde D^{-1/2} H^{(l)} W^{(l)}\\big)","area":"Machine learning","about":"Updates each node's representation from its neighbours' representations.","names":["graph neural network","graph convolutional network","graph convolution","graph attention network","GCN","GNN"],"papers":0,"papers_7d":0,"page":false},{"rank":17,"name":"Gravity model of trade","slug":"gravity-model-of-trade","latex":"X_{ij} = G\\,\\frac{Y_i^{\\beta_1}\\, Y_j^{\\beta_2}}{D_{ij}^{\\beta_3}}","area":"Growth, trade and environment","about":"Trade between two countries rises with their economic size and falls with the 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changing strategy alone.","names":["Nash equilibrium","Nash equilibria"],"papers":4,"papers_7d":0,"page":true},{"rank":28,"name":"Gravity model of trade","slug":"gravity-model-of-trade","latex":"X_{ij} = G\\,\\frac{Y_i^{\\beta_1}\\, Y_j^{\\beta_2}}{D_{ij}^{\\beta_3}}","area":"Growth, trade and environment","about":"Trade between two countries rises with their economic size and falls with the distance between them.","names":["gravity model","gravity equation","structural gravity","PPML"],"papers":3,"papers_7d":0,"page":true},{"rank":28,"name":"Heckman selection model","slug":"heckman-selection-model","latex":"E[y_i \\mid x_i, s_i = 1] = x_i^\\top\\beta + \\rho\\,\\sigma_\\varepsilon\\,\\lambda(z_i^\\top\\gamma),\\quad \\lambda(\\cdot) = \\frac{\\phi(\\cdot)}{\\Phi(\\cdot)}","area":"Causal inference","about":"Corrects for non-random selection of the observed sample with the inverse Mills ratio from a first-stage probit.","names":["Heckman selection","Heckman two-step","Heckman 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per worker grows with saving and shrinks with population growth and depreciation.","names":["Solow model","Solow growth model","Solow-Swan","neoclassical growth model"],"papers":2,"papers_7d":1,"page":true},{"rank":32,"name":"Stochastic frontier analysis","slug":"stochastic-frontier-analysis","latex":"\\ln y_i = f(x_i; \\beta) + v_i - u_i,\\quad u_i \\ge 0","area":"Efficiency and operations","about":"Splits deviations from a production or cost frontier into noise v and inefficiency u.","names":["stochastic frontier","SFA"],"papers":2,"papers_7d":0,"page":true},{"rank":32,"name":"Taylor rule","slug":"taylor-rule","latex":"i_t = r^{*} + \\pi_t + 0.5\\,(\\pi_t - \\pi^{*}) + 0.5\\,(y_t - \\bar y_t)","area":"Macroeconomics","about":"Sets the policy interest rate from inflation's gap to target and the output gap.","names":["Taylor rule","Taylor-type rule"],"papers":2,"papers_7d":0,"page":true},{"rank":38,"name":"Bellman equation","slug":"bellman-equation","latex":"V(s) = \\max_{a}\\left\\{ r(s, a) + \\beta \\sum_{s'} P(s' \\mid s, a)\\, V(s') \\right\\}","area":"Game theory and decision analysis","about":"Recursive condition for the value of a dynamic optimization or Markov decision problem.","names":["Bellman equation","Hamilton-Jacobi-Bellman","HJB equation","Bellman optimality"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Carhart four-factor model","slug":"carhart-four-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + m_i\\,\\mathit{UMD}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds a momentum factor (UMD) to the Fama-French three factors; widely used for fund performance.","names":["Carhart four-factor","Carhart 4-factor","Carhart model","four-factor model"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Data envelopment analysis (DEA)","slug":"data-envelopment-analysis-dea","latex":"\\max_{u, v}\\ \\frac{\\sum_r u_r\\, y_{r0}}{\\sum_i v_i\\, x_{i0}}\\ \\ \\text{s.t.}\\ \\ \\frac{\\sum_r u_r\\, y_{rj}}{\\sum_i v_i\\, x_{ij}} \\le 1\\ \\ \\forall j","area":"Efficiency and operations","about":"Scores the efficiency of each unit as its best ratio of weighted outputs to weighted inputs relative to all units.","names":["data envelopment analysis","DEA model","super-efficiency DEA","slacks-based measure","SBM model","network DEA","DEA"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Environmental Kuznets curve","slug":"environmental-kuznets-curve","latex":"\\ln E_{it} = \\beta_0 + \\beta_1 \\ln Y_{it} + \\beta_2 (\\ln Y_{it})^2 + \\varepsilon_{it}","area":"Growth, trade and environment","about":"Tests whether pollution first rises and then falls as income grows (beta_2 < 0).","names":["environmental Kuznets curve","Kuznets curve","EKC"],"papers":1,"papers_7d":1,"page":true},{"rank":38,"name":"Hodrick-Prescott filter","slug":"hodrick-prescott-filter","latex":"\\min_{\\{\\tau_t\\}} \\sum_{t=1}^{T}(y_t - \\tau_t)^2 + \\lambda \\sum_{t=2}^{T-1}\\big[(\\tau_{t+1} - \\tau_t) - (\\tau_t - \\tau_{t-1})\\big]^2","area":"Time series","about":"Separates a series into a smooth trend and a cyclical component.","names":["Hodrick-Prescott","HP filter","HP-filtered"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"k-means clustering","slug":"k-means-clustering","latex":"\\min_{C_1, \\dots, C_k} \\sum_{j=1}^{k} \\sum_{x \\in C_j} \\lVert x - \\mu_j \\rVert^2","area":"Machine learning","about":"Partitions observations into k clusters around their means.","names":["k-means"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Kalman filter","slug":"kalman-filter","latex":"\\hat x_{t \\mid t} = \\hat x_{t \\mid t-1} + K_t\\,(y_t - H\\,\\hat x_{t \\mid t-1})","area":"Time series","about":"Recursively updates estimates of an unobserved state from noisy observations.","names":["Kalman filter","Kalman filtering","Kalman smoother"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Merton model (distance to default)","slug":"merton-model-distance-to-default","latex":"DD = \\frac{\\ln(V/D) + (\\mu - \\sigma_V^2/2)\\,T}{\\sigma_V\\sqrt{T}}","area":"Asset pricing and risk","about":"Treats equity as a call option on firm assets V; distance to default measures how far assets are from the default point D.","names":["distance to default","Merton model","Merton's model","KMV"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Newsvendor model","slug":"newsvendor-model","latex":"Q^{*} = F^{-1}\\Big(\\frac{c_u}{c_u + c_o}\\Big)","area":"Efficiency and operations","about":"Optimal stock for one selling period under uncertain demand, set by the critical ratio of underage and overage costs.","names":["newsvendor","newsboy problem","newsboy model"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Q-learning","slug":"q-learning","latex":"Q(s, a) \\leftarrow Q(s, a) + \\alpha\\big[r + \\gamma \\max_{a'} Q(s', a') - Q(s, a)\\big]","area":"Machine learning","about":"Reinforcement learning of action values from rewards; deep Q-networks approximate Q with a neural network.","names":["Q-learning","deep Q-network","DQN"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Structural equation modeling (SEM)","slug":"structural-equation-modeling-sem","latex":"\\eta = B\\eta + \\Gamma\\xi + \\zeta,\\quad y = \\Lambda_y\\,\\eta + \\varepsilon","area":"Regression models","about":"Estimates relations among latent constructs measured by several observed indicators; PLS-SEM is a common variant.","names":["structural equation model","structural equation modeling","structural equation modelling","PLS-SEM","partial least squares structural equation","CB-SEM"],"papers":1,"papers_7d":0,"page":true},{"rank":38,"name":"Support vector machine (SVM)","slug":"support-vector-machine-svm","latex":"\\min_{w, b, \\xi}\\ \\tfrac{1}{2}\\lVert w \\rVert^2 + C \\sum_i \\xi_i\\ \\ \\text{s.t.}\\ \\ y_i (w^\\top x_i + b) \\ge 1 - \\xi_i,\\ \\xi_i \\ge 0","area":"Machine learning","about":"Finds the separating hyperplane with the widest margin; support vector regression adapts it to regression.","names":["support vector machine","support vector regression","SVM","SVR"],"papers":1,"papers_7d":1,"page":true},{"rank":50,"name":"Adam optimizer","slug":"adam-optimizer","latex":"\\theta_t = \\theta_{t-1} - \\alpha\\,\\frac{\\hat m_t}{\\sqrt{\\hat v_t} + \\epsilon}","area":"Machine learning","about":"Gradient descent with running averages of the gradient (m) and its square (v).","names":["Adam optimizer","Adam optimiser","Adam optimization","Adam algorithm","AdamW"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Altman Z-score","slug":"altman-z-score","latex":"Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5","area":"Asset pricing and risk","about":"Bankruptcy predictor that weights five accounting ratios (working capital, retained earnings, EBIT, market equity, sales).","names":["Altman Z","Altman's Z"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Amihud illiquidity ratio","slug":"amihud-illiquidity-ratio","latex":"\\mathit{ILLIQ}_i = \\frac{1}{D_i}\\sum_{d=1}^{D_i}\\frac{\\lvert R_{id} \\rvert}{\\mathit{DVOL}_{id}}","area":"Asset pricing and risk","about":"Average absolute daily return per dollar of trading volume: the price impact of trading.","names":["Amihud illiquidity","Amihud's illiquidity","Amihud measure","Amihud's measure","Amihud ratio"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Analytic hierarchy process (AHP)","slug":"analytic-hierarchy-process-ahp","latex":"A\\, w = \\lambda_{\\max}\\, w,\\quad CR = \\frac{(\\lambda_{\\max} - n)/(n - 1)}{RI}","area":"Game theory and decision analysis","about":"Derives criteria weights from pairwise comparisons; CR checks their consistency.","names":["analytic hierarchy process","analytical hierarchy process","AHP"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Bass diffusion model","slug":"bass-diffusion-model","latex":"\\frac{f(t)}{1 - F(t)} = p + q\\, F(t)","area":"Efficiency and operations","about":"Adoption of a new product driven by innovation (p) and imitation (q).","names":["Bass diffusion","Bass model"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Basu asymmetric timeliness","slug":"basu-asymmetric-timeliness","latex":"\\frac{EPS_{it}}{P_{i,t-1}} = \\beta_0 + \\beta_1 D_{it} + \\beta_2 R_{it} + \\beta_3 D_{it} R_{it} + \\varepsilon_{it}","area":"Accounting","about":"Measures accounting conservatism as how much faster earnings reflect bad news (negative returns) than good news.","names":["asymmetric timeliness","Basu model","Basu (1997)","Basu's model"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Bayes' theorem","slug":"bayes-theorem","latex":"P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}","area":"Game theory and decision analysis","about":"Updates the probability of a hypothesis A after observing evidence B.","names":["Bayes' theorem","Bayes theorem","Bayes' rule","Bayes rule","Bayesian updating"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Beneish M-score","slug":"beneish-m-score","latex":"M = -4.84 + 0.92\\,\\mathit{DSRI} + 0.528\\,\\mathit{GMI} + 0.404\\,\\mathit{AQI} + 0.892\\,\\mathit{SGI} + 0.115\\,\\mathit{DEPI} - 0.172\\,\\mathit{SGAI} + 4.679\\,\\mathit{TATA} - 0.327\\,\\mathit{LVGI}","area":"Accounting","about":"Flags likely earnings manipulation from eight financial-statement ratios.","names":["Beneish M-score","Beneish model","Beneish's M-score","M-score"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Best-worst method","slug":"best-worst-method","latex":"\\min\\ \\xi\\ \\ \\text{s.t.}\\ \\ \\lvert w_B - a_{Bj}\\, w_j \\rvert \\le \\xi,\\ \\ \\lvert w_j - a_{jW}\\, w_W \\rvert \\le \\xi,\\ \\ \\sum_j w_j = 1","area":"Game theory and decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Black-Scholes formula","slug":"black-scholes-formula","latex":"C = S_0\\,N(d_1) - K e^{-rT} N(d_2),\\quad d_{1,2} = \\frac{\\ln(S_0/K) + (r \\pm \\sigma^2/2)\\,T}{\\sigma\\sqrt{T}}","area":"Asset pricing and risk","about":"Price of a European call option on a stock with constant volatility and interest rate.","names":["Black-Scholes","Black and Scholes"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Capital asset pricing model (CAPM)","slug":"capital-asset-pricing-model-capm","latex":"E[R_i] = R_f + \\beta_i\\,(E[R_m] - R_f)","area":"Asset pricing and risk","about":"Expected return of an asset as the risk-free rate plus its market beta times the market risk premium.","names":["capital asset pricing model","CAPM"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"CES production function","slug":"ces-production-function","latex":"Y = A\\big[\\alpha K^{\\rho} + (1 - \\alpha) L^{\\rho}\\big]^{1/\\rho}","area":"Growth, trade and environment","about":"Production (or utility) with a constant elasticity of substitution 1/(1 - rho) between inputs.","names":["constant elasticity of substitution","CES production","CES utility","CES function"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Cobb-Douglas production function","slug":"cobb-douglas-production-function","latex":"Y = A\\, K^{\\alpha} L^{1 - \\alpha}","area":"Growth, trade and environment","about":"Output from capital and labour with constant output shares.","names":["Cobb-Douglas"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Consumption Euler equation","slug":"consumption-euler-equation","latex":"u'(c_t) = \\beta\\,E_t\\big[(1 + r_{t+1})\\,u'(c_{t+1})\\big]","area":"Macroeconomics","about":"Optimal saving condition: the marginal utility of consuming today equals the discounted expected return of saving it.","names":["Euler equation","consumption Euler"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Contrastive loss (InfoNCE)","slug":"contrastive-loss-infonce","latex":"\\mathcal{L} = -\\log \\frac{\\exp(\\mathrm{sim}(z_i, z_j)/\\tau)}{\\sum_{k \\ne i} \\exp(\\mathrm{sim}(z_i, z_k)/\\tau)}","area":"Machine learning","about":"Pulls representations of matching pairs together and pushes others apart.","names":["InfoNCE","contrastive loss","contrastive learning","NT-Xent"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Convolutional neural network (CNN)","slug":"convolutional-neural-network-cnn","latex":"(I * K)(i, j) = \\sum_{m}\\sum_{n} I(i + m,\\, j + n)\\, K(m, n)","area":"Machine learning","about":"Networks built from learned convolution filters, standard for images and other grid data.","names":["convolutional neural network","CNN","ConvNet"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + U_2},\\quad T = \\alpha U_1 + \\beta U_2,\\quad D = \\sqrt{C\\, T}","area":"Game theory and decision analysis","about":"Measures how well two systems (for example the economy and the environment) develop together.","names":["coupling coordination","coupled coordination"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"CoVaR (systemic risk)","slug":"covar-systemic-risk","latex":"\\Pr\\big(X^{\\mathrm{sys}} \\le \\mathrm{CoVaR}_q^{\\mathrm{sys} \\mid i} \\mid X^{i} = \\mathrm{VaR}_q^{i}\\big) = q","area":"Asset pricing and risk","about":"Value at risk of the financial system conditional on an institution being in distress; Delta CoVaR measures its contribution.","names":["CoVaR","delta CoVaR"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Covered interest parity","slug":"covered-interest-parity","latex":"\\frac{F_t}{S_t} = \\frac{1 + i_t}{1 + i_t^{*}}","area":"Macroeconomics","about":"The forward premium of a currency equals the interest rate differential; deviations signal funding frictions.","names":["covered interest parity","covered interest rate parity","CIP deviation"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Cox proportional hazards model","slug":"cox-proportional-hazards-model","latex":"h(t \\mid x) = h_0(t)\\,\\exp(x^\\top\\beta)","area":"Regression models","about":"Models the hazard of an event over time as a baseline hazard scaled by the regressors.","names":["Cox proportional hazard","proportional hazards model","Cox regression","Cox model","Cox hazard model"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Cross-entropy loss","slug":"cross-entropy-loss","latex":"\\mathcal{L} = -\\sum_{c=1}^{C} y_c \\log \\hat y_c","area":"Machine learning","about":"Standard loss for classification: the negative log-probability of the true class.","names":["cross-entropy"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Dechow-Dichev accruals quality","slug":"dechow-dichev-accruals-quality","latex":"\\Delta WC_{it} = \\beta_0 + \\beta_1\\, CFO_{i,t-1} + \\beta_2\\, CFO_{it} + \\beta_3\\, CFO_{i,t+1} + \\varepsilon_{it}","area":"Accounting","about":"Measures how well working-capital accruals map into past, current and future cash flows.","names":["Dechow and Dichev","Dechow-Dichev","accruals quality","accrual quality"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"DEMATEL","slug":"dematel","latex":"T = X\\,(I - X)^{-1}","area":"Game theory and decision analysis","about":"Maps cause-and-effect relations among factors from a normalized direct-influence matrix X.","names":["DEMATEL"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Denoising diffusion model","slug":"denoising-diffusion-model","latex":"\\mathcal{L} = E_{t, x_0, \\epsilon}\\Big[\\left\\lVert \\epsilon - \\epsilon_\\theta\\big(\\sqrt{\\bar\\alpha_t}\\, x_0 + \\sqrt{1 - \\bar\\alpha_t}\\, \\epsilon,\\ t\\big) \\right\\rVert^2\\Big]","area":"Machine learning","about":"Generative model that learns to remove noise step by step; the basis of current image generators.","names":["denoising diffusion","diffusion probabilistic","latent diffusion","score-based generative","Stable Diffusion"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Dividend discount (Gordon growth) model","slug":"dividend-discount-gordon-growth-model","latex":"P_0 = \\frac{D_1}{r - g}","area":"Asset pricing and risk","about":"Values a stock as next year's dividend divided by the discount rate minus the dividend growth rate.","names":["dividend discount model","Gordon growth model"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Economic order quantity (EOQ)","slug":"economic-order-quantity-eoq","latex":"Q^{*} = \\sqrt{\\frac{2 D S}{H}}","area":"Efficiency and operations","about":"Order size that minimizes ordering plus holding costs.","names":["economic order quantity","EOQ"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Entropy weight method","slug":"entropy-weight-method","latex":"e_j = -\\frac{1}{\\ln n}\\sum_{i=1}^{n} p_{ij}\\ln p_{ij},\\quad w_j = \\frac{1 - e_j}{\\sum_k (1 - e_k)}","area":"Game theory and decision analysis","about":"Weights indicators by how much their values vary across units, often to build composite indices.","names":["entropy weight","entropy weighting","entropy method"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Event study (abnormal returns)","slug":"event-study-abnormal-returns","latex":"AR_{it} = R_{it} - (\\hat\\alpha_i + \\hat\\beta_i R_{mt}),\\quad CAR_i = \\sum_{t=t_1}^{t_2} AR_{it}","area":"Causal inference","about":"Measures returns beyond what a market model predicts around an event such as an announcement.","names":["abnormal return","cumulative abnormal return","buy-and-hold abnormal return"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Fama-French five-factor model","slug":"fama-french-five-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + r_i\\,\\mathit{RMW}_t + c_i\\,\\mathit{CMA}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds profitability (RMW) and investment (CMA) factors to the three-factor model.","names":["Fama-French five-factor","Fama and French five-factor","Fama-French 5-factor","five-factor model","FF5"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Fama-French three-factor model","slug":"fama-french-three-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Explains excess returns with the market, size (SMB) and value (HML) factors.","names":["Fama-French three-factor","Fama and French three-factor","Fama-French 3-factor","Fama and French 3-factor","three-factor model","FF3"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Fisher equation","slug":"fisher-equation","latex":"i_t \\approx r_t + E_t[\\pi_{t+1}]","area":"Macroeconomics","about":"The nominal interest rate equals the real rate plus expected inflation.","names":["Fisher equation","Fisher effect","Fisher hypothesis"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Gated recurrent unit (GRU)","slug":"gated-recurrent-unit-gru","latex":"h_t = (1 - z_t) \\odot h_{t-1} + z_t \\odot \\tilde h_t","area":"Machine learning","about":"A simpler gated recurrent cell with update and reset gates.","names":["gated recurrent unit","GRU"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Generative adversarial network (GAN)","slug":"generative-adversarial-network-gan","latex":"\\min_G \\max_D\\ E_x\\big[\\log D(x)\\big] + E_z\\big[\\log\\big(1 - D(G(z))\\big)\\big]","area":"Machine learning","about":"A generator and a discriminator trained against each other.","names":["generative adversarial","GAN"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Gradient descent","slug":"gradient-descent","latex":"\\theta_{t+1} = \\theta_t - \\eta\\, \\nabla_\\theta \\mathcal{L}(\\theta_t)","area":"Machine learning","about":"Moves parameters a step against the gradient of the loss; stochastic gradient descent uses mini-batches.","names":["gradient descent","SGD"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Graph neural network (graph convolution)","slug":"graph-neural-network-graph-convolution","latex":"H^{(l+1)} = \\sigma\\big(\\tilde D^{-1/2} \\tilde A\\, \\tilde D^{-1/2} H^{(l)} W^{(l)}\\big)","area":"Machine learning","about":"Updates each node's representation from its neighbours' representations.","names":["graph neural network","graph convolutional network","graph convolution","graph attention network","GCN","GNN"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Herfindahl-Hirschman index","slug":"herfindahl-hirschman-index","latex":"\\mathit{HHI} = \\sum_{i=1}^{N} s_i^2","area":"Labour, inequality and competition","about":"Market concentration as the sum of squared market shares.","names":["Herfindahl","HHI"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Heston stochastic volatility model","slug":"heston-stochastic-volatility-model","latex":"dv_t = \\kappa\\,(\\theta - v_t)\\,dt + \\xi\\sqrt{v_t}\\,dW_t^{v}","area":"Asset pricing and risk","about":"Option pricing model in which the variance follows a mean-reverting square-root process.","names":["Heston model","Heston stochastic volatility","Heston's model"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Jensen's alpha","slug":"jensen-s-alpha","latex":"\\alpha_p = R_p - \\big[R_f + \\beta_p\\,(R_m - R_f)\\big]","area":"Asset pricing and risk","about":"A portfolio's return beyond what the CAPM predicts for its beta.","names":["Jensen's alpha","Jensen alpha"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Kaya identity","slug":"kaya-identity","latex":"\\mathrm{CO_2} = P \\times \\frac{\\mathit{GDP}}{P} \\times \\frac{E}{\\mathit{GDP}} \\times \\frac{\\mathrm{CO_2}}{E}","area":"Growth, trade and environment","about":"Decomposes carbon emissions into population, income per person, energy intensity and carbon intensity.","names":["Kaya identity"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Kullback-Leibler divergence","slug":"kullback-leibler-divergence","latex":"D_{\\mathrm{KL}}(P \\parallel Q) = \\sum_x P(x) \\log \\frac{P(x)}{Q(x)}","area":"Machine learning","about":"How much one probability distribution differs from another.","names":["Kullback-Leibler","KL divergence"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Lerner index","slug":"lerner-index","latex":"L = \\frac{P - MC}{P}","area":"Labour, inequality and competition","about":"Market power as the markup of price over marginal cost.","names":["Lerner index"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Linear and integer programming","slug":"linear-and-integer-programming","latex":"\\min_{x}\\ c^\\top x\\ \\ \\text{s.t.}\\ \\ A x \\le b,\\ x \\ge 0,\\ x_j \\in \\mathbb{Z}\\ (j \\in I)","area":"Efficiency and operations","about":"Optimizes a linear objective under linear constraints, with some variables restricted to integers.","names":["linear programming","linear program","integer programming","integer program","MILP","MINLP","mixed-integer"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Little's law","slug":"little-s-law","latex":"L = \\lambda W","area":"Efficiency and operations","about":"Average number in a queueing system equals the arrival rate times the average time spent in it.","names":["Little's law","Little's formula"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Low-rank adaptation (LoRA)","slug":"low-rank-adaptation-lora","latex":"W = W_0 + B A,\\quad B \\in \\mathbb{R}^{d \\times r},\\ A \\in \\mathbb{R}^{r \\times k},\\ r \\ll \\min(d, k)","area":"Machine learning","about":"Fine-tunes a large model by learning a small low-rank update to its weights.","names":["low-rank adaptation","LoRA"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Mean-variance portfolio (Markowitz)","slug":"mean-variance-portfolio-markowitz","latex":"\\min_{w}\\ w^\\top \\Sigma\\, w\\ \\ \\text{s.t.}\\ \\ w^\\top \\mu = \\mu_p,\\ \\ w^\\top \\mathbf{1} = 1","area":"Asset pricing and risk","about":"Chooses portfolio weights with the lowest variance for a target expected return.","names":["mean-variance","Markowitz","modern portfolio theory"],"papers":0,"papers_7d":0,"page":false},{"rank":50,"name":"Mincer earnings equation","slug":"mincer-earnings-equation","latex":"\\ln w_i = \\beta_0 + \\beta_1 S_i + \\beta_2 X_i + \\beta_3 X_i^2 + \\varepsilon_i","area":"Labour, inequality and competition","about":"Log wages as a function of years of schooling S and 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GMM","Arellano-Bond"],"papers":6,"papers_7d":0,"page":true},{"rank":9,"name":"Probit model","slug":"probit-model","latex":"\\Pr(y = 1 \\mid x) = \\Phi(x^\\top\\beta)","area":"Regression models","about":"Models the probability of a binary outcome with the standard normal distribution function.","names":["probit"],"papers":6,"papers_7d":1,"page":true},{"rank":11,"name":"Gradient boosting (XGBoost)","slug":"gradient-boosting-xgboost","latex":"\\mathcal{L} = \\sum_i l(y_i, \\hat y_i) + \\sum_k \\Omega(f_k),\\quad \\Omega(f) = \\gamma T + \\tfrac{1}{2}\\lambda \\lVert w \\rVert^2","area":"Machine learning","about":"Adds trees one at a time, each fitted to the errors of the ensemble so far, with a penalty on tree complexity.","names":["XGBoost","gradient boosting","LightGBM","CatBoost","GBDT"],"papers":4,"papers_7d":1,"page":true},{"rank":11,"name":"Quantile regression","slug":"quantile-regression","latex":"\\hat\\beta_\\tau = \\operatorname*{arg\\,min}_{\\beta} \\sum_{i} \\rho_\\tau(y_i - x_i^\\top\\beta),\\quad \\rho_\\tau(u) = u\\,(\\tau - \\mathbf{1}\\{u < 0\\})","area":"Regression models","about":"Estimates how regressors shift a chosen quantile of the outcome rather than its mean.","names":["quantile regression","quantile-on-quantile"],"papers":4,"papers_7d":0,"page":true},{"rank":11,"name":"Total factor productivity (Solow residual)","slug":"total-factor-productivity-solow-residual","latex":"\\ln A_t = \\ln Y_t - \\alpha \\ln K_t - (1 - \\alpha) \\ln L_t","area":"Growth, trade and environment","about":"The part of output growth not explained by measured inputs.","names":["total factor productivity","Solow residual","TFP"],"papers":4,"papers_7d":0,"page":true},{"rank":14,"name":"Autoregressive distributed lag (ARDL)","slug":"autoregressive-distributed-lag-ardl","latex":"y_t = \\alpha + \\sum_{i=1}^{p}\\phi_i\\, y_{t-i} + \\sum_{j=0}^{q}\\beta_j^\\top x_{t-j} + \\varepsilon_t","area":"Time series","about":"Regresses a series on its own lags and current and lagged regressors; the bounds test checks for a long-run relation.","names":["autoregressive distributed lag","ARDL","NARDL","QARDL","CS-ARDL"],"papers":3,"papers_7d":0,"page":true},{"rank":14,"name":"Cointegration and error correction (VECM)","slug":"cointegration-and-error-correction-vecm","latex":"\\Delta y_t = \\Pi\\, y_{t-1} + \\sum_{i=1}^{p-1}\\Gamma_i\\,\\Delta y_{t-i} + \\varepsilon_t","area":"Time series","about":"Models series that share a long-run equilibrium; Pi holds the cointegrating relations and adjustment speeds.","names":["cointegration","co-integration","error correction model","vector error correction","VECM","Johansen test"],"papers":3,"papers_7d":0,"page":true},{"rank":14,"name":"Heckman selection model","slug":"heckman-selection-model","latex":"E[y_i \\mid x_i, s_i = 1] = x_i^\\top\\beta + \\rho\\,\\sigma_\\varepsilon\\,\\lambda(z_i^\\top\\gamma),\\quad \\lambda(\\cdot) = \\frac{\\phi(\\cdot)}{\\Phi(\\cdot)}","area":"Causal inference","about":"Corrects for non-random selection of the observed sample with the inverse Mills ratio from a first-stage probit.","names":["Heckman selection","Heckman two-step","Heckman two-stage","Heckman correction","Heckman model","inverse Mills ratio","sample selection model"],"papers":3,"papers_7d":1,"page":true},{"rank":14,"name":"Long short-term memory (LSTM)","slug":"long-short-term-memory-lstm","latex":"c_t = f_t \\odot c_{t-1} + i_t \\odot \\tilde c_t,\\quad h_t = o_t \\odot \\tanh(c_t)","area":"Machine learning","about":"Recurrent network cell whose gates decide what to keep, add and output at each step.","names":["LSTM","long short-term memory","BiLSTM","Bi-LSTM"],"papers":3,"papers_7d":1,"page":true},{"rank":14,"name":"Vector autoregression (VAR)","slug":"vector-autoregression-var","latex":"y_t = c + \\sum_{i=1}^{p} A_i\\, y_{t-i} + \\varepsilon_t","area":"Time series","about":"Models several time series jointly, each as a function of the lags of all of them.","names":["vector autoregression","vector autoregressive","SVAR","TVP-VAR","panel VAR","Bayesian VAR","structural VAR","VAR model","VAR framework","VAR approach","VAR analysis"],"papers":3,"papers_7d":0,"page":true},{"rank":19,"name":"Gini coefficient","slug":"gini-coefficient","latex":"G = \\frac{\\sum_{i=1}^{n}\\sum_{j=1}^{n} \\lvert x_i - x_j \\rvert}{2 n^2 \\bar x}","area":"Labour, inequality and competition","about":"Inequality measure from 0 (equal) to 1 (one unit has everything).","names":["Gini coefficient","Gini index"],"papers":2,"papers_7d":0,"page":true},{"rank":19,"name":"Granger causality","slug":"granger-causality","latex":"y_t = \\sum_{i=1}^{p} a_i\\, y_{t-i} + \\sum_{j=1}^{p} b_j\\, x_{t-j} + \\varepsilon_t,\\quad H_0: b_1 = \\dots = b_p = 0","area":"Time series","about":"Tests whether past values of x help predict y beyond y's own past.","names":["Granger causality","Granger cause","Granger causal","Granger non-causality"],"papers":2,"papers_7d":0,"page":true},{"rank":19,"name":"Herfindahl-Hirschman index","slug":"herfindahl-hirschman-index","latex":"\\mathit{HHI} = \\sum_{i=1}^{N} s_i^2","area":"Labour, inequality and competition","about":"Market concentration as the sum of squared market shares.","names":["Herfindahl","HHI"],"papers":2,"papers_7d":0,"page":true},{"rank":19,"name":"Principal component analysis (PCA)","slug":"principal-component-analysis-pca","latex":"\\max_{\\lVert w \\rVert = 1}\\ w^\\top \\Sigma\\, w","area":"Machine learning","about":"Finds the orthogonal directions of largest variance in the data.","names":["principal component analysis","principal components analysis","PCA"],"papers":2,"papers_7d":1,"page":true},{"rank":19,"name":"Random forest","slug":"random-forest","latex":"\\hat f(x) = \\frac{1}{B}\\sum_{b=1}^{B} T_b(x)","area":"Machine learning","about":"Averages many decision trees grown on bootstrap samples with random feature subsets.","names":["random forest"],"papers":2,"papers_7d":1,"page":true},{"rank":19,"name":"Shapley value (SHAP)","slug":"shapley-value-shap","latex":"\\phi_i(v) = \\sum_{S \\subseteq N \\setminus \\{i\\}} \\frac{\\lvert S \\rvert!\\,(n - \\lvert S \\rvert - 1)!}{n!}\\big[v(S \\cup \\{i\\}) - v(S)\\big]","area":"Game theory and decision analysis","about":"A player's average marginal contribution over all coalitions; SHAP uses it to explain machine-learning predictions.","names":["Shapley value","SHAP","Shapley additive explanation"],"papers":2,"papers_7d":0,"page":true},{"rank":25,"name":"ARIMA","slug":"arima","latex":"\\phi(L)\\,(1 - L)^{d}\\, y_t = \\theta(L)\\,\\varepsilon_t","area":"Time series","about":"Autoregressive integrated moving-average model of a time series, with lag operator L and differencing order d.","names":["ARIMA","SARIMA","ARMA","ARFIMA","autoregressive integrated moving average","autoregressive moving average"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Cox proportional hazards model","slug":"cox-proportional-hazards-model","latex":"h(t \\mid x) = h_0(t)\\,\\exp(x^\\top\\beta)","area":"Regression models","about":"Models the hazard of an event over time as a baseline hazard scaled by the regressors.","names":["Cox proportional hazard","proportional hazards model","Cox regression","Cox model","Cox hazard model"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Event study (abnormal returns)","slug":"event-study-abnormal-returns","latex":"AR_{it} = R_{it} - (\\hat\\alpha_i + \\hat\\beta_i R_{mt}),\\quad CAR_i = \\sum_{t=t_1}^{t_2} AR_{it}","area":"Causal inference","about":"Measures returns beyond what a market model predicts around an event such as an announcement.","names":["abnormal return","cumulative abnormal return","buy-and-hold abnormal return"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"GARCH","slug":"garch","latex":"\\sigma_t^2 = \\omega + \\alpha\\,\\varepsilon_{t-1}^2 + \\beta\\,\\sigma_{t-1}^2","area":"Time series","about":"Models time-varying volatility: today's variance depends on yesterday's shock and variance (GARCH(1,1)).","names":["GARCH","EGARCH","TGARCH","FIGARCH","MGARCH","generalized autoregressive conditional heteroskedasticity","generalized autoregressive conditional heteroscedasticity"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Graph neural network (graph convolution)","slug":"graph-neural-network-graph-convolution","latex":"H^{(l+1)} = \\sigma\\big(\\tilde D^{-1/2} \\tilde A\\, \\tilde D^{-1/2} H^{(l)} W^{(l)}\\big)","area":"Machine learning","about":"Updates each node's representation from its neighbours' representations.","names":["graph neural network","graph convolutional network","graph convolution","graph attention network","GCN","GNN"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"LASSO","slug":"lasso","latex":"\\hat\\beta = \\operatorname*{arg\\,min}_{\\beta}\\ \\lVert y - X\\beta \\rVert_2^2 + \\lambda \\lVert \\beta \\rVert_1","area":"Regression models","about":"Regression with an L1 penalty that shrinks coefficients and sets many of them to exactly zero.","names":["Lasso","least absolute shrinkage"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Markov-switching model","slug":"markov-switching-model","latex":"y_t = \\mu_{s_t} + \\varepsilon_t,\\quad \\Pr(s_t = j \\mid s_{t-1} = i) = p_{ij}","area":"Time series","about":"Lets a model's parameters change with an unobserved regime that follows a Markov chain.","names":["Markov switching","Markov regime switching","regime switching model"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Nash equilibrium","slug":"nash-equilibrium","latex":"u_i(s_i^{*}, s_{-i}^{*}) \\ge u_i(s_i, s_{-i}^{*})\\quad \\forall i,\\ \\forall s_i","area":"Game theory and decision analysis","about":"No player can gain by changing strategy alone.","names":["Nash equilibrium","Nash equilibria"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Stackelberg game","slug":"stackelberg-game","latex":"\\max_{x_L}\\ \\pi_L\\big(x_L, x_F^{*}(x_L)\\big),\\quad x_F^{*}(x_L) = \\operatorname*{arg\\,max}_{x_F}\\ \\pi_F(x_L, x_F)","area":"Game theory and decision analysis","about":"A leader moves first anticipating the follower's best response; common in supply-chain models.","names":["Stackelberg"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Support vector machine (SVM)","slug":"support-vector-machine-svm","latex":"\\min_{w, b, \\xi}\\ \\tfrac{1}{2}\\lVert w \\rVert^2 + C \\sum_i \\xi_i\\ \\ \\text{s.t.}\\ \\ y_i (w^\\top x_i + b) \\ge 1 - \\xi_i,\\ \\xi_i \\ge 0","area":"Machine learning","about":"Finds the separating hyperplane with the widest margin; support vector regression adapts it to regression.","names":["support vector machine","support vector regression","SVM","SVR"],"papers":1,"papers_7d":0,"page":true},{"rank":25,"name":"Synthetic control method","slug":"synthetic-control-method","latex":"\\hat Y^{N}_{1t} = \\sum_{j=2}^{J+1} w_j^{*}\\, Y_{jt},\\quad w_j^{*} \\ge 0,\\ \\sum_j w_j^{*} = 1","area":"Causal inference","about":"Builds the counterfactual for a treated unit as a weighted average of untreated units.","names":["synthetic control"],"papers":1,"papers_7d":0,"page":true},{"rank":36,"name":"Adam optimizer","slug":"adam-optimizer","latex":"\\theta_t = \\theta_{t-1} - \\alpha\\,\\frac{\\hat m_t}{\\sqrt{\\hat v_t} + \\epsilon}","area":"Machine learning","about":"Gradient descent with running averages of the gradient (m) and its square (v).","names":["Adam optimizer","Adam optimiser","Adam optimization","Adam algorithm","AdamW"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Altman Z-score","slug":"altman-z-score","latex":"Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5","area":"Asset pricing and risk","about":"Bankruptcy predictor that weights five accounting ratios (working capital, retained earnings, EBIT, market equity, sales).","names":["Altman Z","Altman's Z"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Amihud illiquidity ratio","slug":"amihud-illiquidity-ratio","latex":"\\mathit{ILLIQ}_i = \\frac{1}{D_i}\\sum_{d=1}^{D_i}\\frac{\\lvert R_{id} \\rvert}{\\mathit{DVOL}_{id}}","area":"Asset pricing and risk","about":"Average absolute daily return per dollar of trading volume: the price impact of trading.","names":["Amihud illiquidity","Amihud's illiquidity","Amihud measure","Amihud's measure","Amihud ratio"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Analytic hierarchy process (AHP)","slug":"analytic-hierarchy-process-ahp","latex":"A\\, w = \\lambda_{\\max}\\, w,\\quad CR = \\frac{(\\lambda_{\\max} - n)/(n - 1)}{RI}","area":"Game theory and decision analysis","about":"Derives criteria weights from pairwise comparisons; CR checks their consistency.","names":["analytic hierarchy process","analytical hierarchy process","AHP"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Bass diffusion model","slug":"bass-diffusion-model","latex":"\\frac{f(t)}{1 - F(t)} = p + q\\, F(t)","area":"Efficiency and operations","about":"Adoption of a new product driven by innovation (p) and imitation (q).","names":["Bass diffusion","Bass model"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Basu asymmetric timeliness","slug":"basu-asymmetric-timeliness","latex":"\\frac{EPS_{it}}{P_{i,t-1}} = \\beta_0 + \\beta_1 D_{it} + \\beta_2 R_{it} + \\beta_3 D_{it} R_{it} + \\varepsilon_{it}","area":"Accounting","about":"Measures accounting conservatism as how much faster earnings reflect bad news (negative returns) than good news.","names":["asymmetric timeliness","Basu model","Basu (1997)","Basu's model"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Bayes' theorem","slug":"bayes-theorem","latex":"P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}","area":"Game theory and decision analysis","about":"Updates the probability of a hypothesis A after observing evidence B.","names":["Bayes' theorem","Bayes theorem","Bayes' rule","Bayes rule","Bayesian updating"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Bellman equation","slug":"bellman-equation","latex":"V(s) = \\max_{a}\\left\\{ r(s, a) + \\beta \\sum_{s'} P(s' \\mid s, a)\\, V(s') \\right\\}","area":"Game theory and decision analysis","about":"Recursive condition for the value of a dynamic optimization or Markov decision problem.","names":["Bellman equation","Hamilton-Jacobi-Bellman","HJB equation","Bellman optimality"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Beneish M-score","slug":"beneish-m-score","latex":"M = -4.84 + 0.92\\,\\mathit{DSRI} + 0.528\\,\\mathit{GMI} + 0.404\\,\\mathit{AQI} + 0.892\\,\\mathit{SGI} + 0.115\\,\\mathit{DEPI} - 0.172\\,\\mathit{SGAI} + 4.679\\,\\mathit{TATA} - 0.327\\,\\mathit{LVGI}","area":"Accounting","about":"Flags likely earnings manipulation from eight financial-statement ratios.","names":["Beneish M-score","Beneish model","Beneish's M-score","M-score"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Best-worst method","slug":"best-worst-method","latex":"\\min\\ \\xi\\ \\ \\text{s.t.}\\ \\ \\lvert w_B - a_{Bj}\\, w_j \\rvert \\le \\xi,\\ \\ \\lvert w_j - a_{jW}\\, w_W \\rvert \\le \\xi,\\ \\ \\sum_j w_j = 1","area":"Game theory and decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Black-Scholes formula","slug":"black-scholes-formula","latex":"C = S_0\\,N(d_1) - K e^{-rT} N(d_2),\\quad d_{1,2} = \\frac{\\ln(S_0/K) + (r \\pm \\sigma^2/2)\\,T}{\\sigma\\sqrt{T}}","area":"Asset pricing and risk","about":"Price of a European call option on a stock with constant volatility and interest rate.","names":["Black-Scholes","Black and Scholes"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Capital asset pricing model (CAPM)","slug":"capital-asset-pricing-model-capm","latex":"E[R_i] = R_f + \\beta_i\\,(E[R_m] - R_f)","area":"Asset pricing and risk","about":"Expected return of an asset as the risk-free rate plus its market beta times the market risk premium.","names":["capital asset pricing model","CAPM"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Carhart four-factor model","slug":"carhart-four-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + m_i\\,\\mathit{UMD}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds a momentum factor (UMD) to the Fama-French three factors; widely used for fund performance.","names":["Carhart four-factor","Carhart 4-factor","Carhart model","four-factor model"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"CES production function","slug":"ces-production-function","latex":"Y = A\\big[\\alpha K^{\\rho} + (1 - \\alpha) L^{\\rho}\\big]^{1/\\rho}","area":"Growth, trade and environment","about":"Production (or utility) with a constant elasticity of substitution 1/(1 - rho) between inputs.","names":["constant elasticity of substitution","CES production","CES utility","CES function"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Cobb-Douglas production function","slug":"cobb-douglas-production-function","latex":"Y = A\\, K^{\\alpha} L^{1 - \\alpha}","area":"Growth, trade and environment","about":"Output from capital and labour with constant output shares.","names":["Cobb-Douglas"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Consumption Euler equation","slug":"consumption-euler-equation","latex":"u'(c_t) = \\beta\\,E_t\\big[(1 + r_{t+1})\\,u'(c_{t+1})\\big]","area":"Macroeconomics","about":"Optimal saving condition: the marginal utility of consuming today equals the discounted expected return of saving it.","names":["Euler equation","consumption Euler"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Contrastive loss (InfoNCE)","slug":"contrastive-loss-infonce","latex":"\\mathcal{L} = -\\log \\frac{\\exp(\\mathrm{sim}(z_i, z_j)/\\tau)}{\\sum_{k \\ne i} \\exp(\\mathrm{sim}(z_i, z_k)/\\tau)}","area":"Machine learning","about":"Pulls representations of matching pairs together and pushes others apart.","names":["InfoNCE","contrastive loss","contrastive learning","NT-Xent"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Convolutional neural network (CNN)","slug":"convolutional-neural-network-cnn","latex":"(I * K)(i, j) = \\sum_{m}\\sum_{n} I(i + m,\\, j + n)\\, K(m, n)","area":"Machine learning","about":"Networks built from learned convolution filters, standard for images and other grid data.","names":["convolutional neural network","CNN","ConvNet"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + U_2},\\quad T = \\alpha U_1 + \\beta U_2,\\quad D = \\sqrt{C\\, T}","area":"Game theory and decision analysis","about":"Measures how well two systems (for example the economy and the environment) develop together.","names":["coupling coordination","coupled coordination"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"CoVaR (systemic risk)","slug":"covar-systemic-risk","latex":"\\Pr\\big(X^{\\mathrm{sys}} \\le \\mathrm{CoVaR}_q^{\\mathrm{sys} \\mid i} \\mid X^{i} = \\mathrm{VaR}_q^{i}\\big) = q","area":"Asset pricing and risk","about":"Value at risk of the financial system conditional on an institution being in distress; Delta CoVaR measures its contribution.","names":["CoVaR","delta CoVaR"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Covered interest parity","slug":"covered-interest-parity","latex":"\\frac{F_t}{S_t} = \\frac{1 + i_t}{1 + i_t^{*}}","area":"Macroeconomics","about":"The forward premium of a currency equals the interest rate differential; deviations signal funding frictions.","names":["covered interest parity","covered interest rate parity","CIP deviation"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Cross-entropy loss","slug":"cross-entropy-loss","latex":"\\mathcal{L} = -\\sum_{c=1}^{C} y_c \\log \\hat y_c","area":"Machine learning","about":"Standard loss for classification: the negative log-probability of the true class.","names":["cross-entropy"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Data envelopment analysis (DEA)","slug":"data-envelopment-analysis-dea","latex":"\\max_{u, v}\\ \\frac{\\sum_r u_r\\, y_{r0}}{\\sum_i v_i\\, x_{i0}}\\ \\ \\text{s.t.}\\ \\ \\frac{\\sum_r u_r\\, y_{rj}}{\\sum_i v_i\\, x_{ij}} \\le 1\\ \\ \\forall j","area":"Efficiency and operations","about":"Scores the efficiency of each unit as its best ratio of weighted outputs to weighted inputs relative to all units.","names":["data envelopment analysis","DEA model","super-efficiency DEA","slacks-based measure","SBM model","network DEA","DEA"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Dechow-Dichev accruals quality","slug":"dechow-dichev-accruals-quality","latex":"\\Delta WC_{it} = \\beta_0 + \\beta_1\\, CFO_{i,t-1} + \\beta_2\\, CFO_{it} + \\beta_3\\, CFO_{i,t+1} + \\varepsilon_{it}","area":"Accounting","about":"Measures how well working-capital accruals map into past, current and future cash flows.","names":["Dechow and Dichev","Dechow-Dichev","accruals quality","accrual quality"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"DEMATEL","slug":"dematel","latex":"T = X\\,(I - X)^{-1}","area":"Game theory and decision analysis","about":"Maps cause-and-effect relations among factors from a normalized direct-influence matrix X.","names":["DEMATEL"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Denoising diffusion model","slug":"denoising-diffusion-model","latex":"\\mathcal{L} = E_{t, x_0, \\epsilon}\\Big[\\left\\lVert \\epsilon - \\epsilon_\\theta\\big(\\sqrt{\\bar\\alpha_t}\\, x_0 + \\sqrt{1 - \\bar\\alpha_t}\\, \\epsilon,\\ t\\big) \\right\\rVert^2\\Big]","area":"Machine learning","about":"Generative model that learns to remove noise step by step; the basis of current image generators.","names":["denoising diffusion","diffusion probabilistic","latent diffusion","score-based generative","Stable Diffusion"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Dividend discount (Gordon growth) model","slug":"dividend-discount-gordon-growth-model","latex":"P_0 = \\frac{D_1}{r - g}","area":"Asset pricing and risk","about":"Values a stock as next year's dividend divided by the discount rate minus the dividend growth rate.","names":["dividend discount model","Gordon growth model"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Economic order quantity (EOQ)","slug":"economic-order-quantity-eoq","latex":"Q^{*} = \\sqrt{\\frac{2 D S}{H}}","area":"Efficiency and operations","about":"Order size that minimizes ordering plus holding costs.","names":["economic order quantity","EOQ"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Entropy weight method","slug":"entropy-weight-method","latex":"e_j = -\\frac{1}{\\ln n}\\sum_{i=1}^{n} p_{ij}\\ln p_{ij},\\quad w_j = \\frac{1 - e_j}{\\sum_k (1 - e_k)}","area":"Game theory and decision analysis","about":"Weights indicators by how much their values vary across units, often to build composite indices.","names":["entropy weight","entropy weighting","entropy method"],"papers":0,"papers_7d":0,"page":false},{"rank":36,"name":"Environmental Kuznets curve","slug":"environmental-kuznets-curve","latex":"\\ln E_{it} = \\beta_0 + \\beta_1 \\ln Y_{it} + \\beta_2 (\\ln Y_{it})^2 + \\varepsilon_{it}","area":"Growth, trade and environment","about":"Tests whether pollution first rises and then falls as income grows (beta_2 < 0).","names":["environmental Kuznets curve","Kuznets 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decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Black-Scholes formula","slug":"black-scholes-formula","latex":"C = S_0\\,N(d_1) - K e^{-rT} N(d_2),\\quad d_{1,2} = \\frac{\\ln(S_0/K) + (r \\pm \\sigma^2/2)\\,T}{\\sigma\\sqrt{T}}","area":"Asset pricing and risk","about":"Price of a European call option on a stock with constant volatility and interest rate.","names":["Black-Scholes","Black and Scholes"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Capital asset pricing model (CAPM)","slug":"capital-asset-pricing-model-capm","latex":"E[R_i] = R_f + \\beta_i\\,(E[R_m] - R_f)","area":"Asset pricing and risk","about":"Expected return of an asset as the risk-free rate plus its market beta times the market risk premium.","names":["capital asset pricing model","CAPM"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Carhart four-factor model","slug":"carhart-four-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + m_i\\,\\mathit{UMD}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds a momentum factor (UMD) to the Fama-French three factors; widely used for fund performance.","names":["Carhart four-factor","Carhart 4-factor","Carhart model","four-factor model"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"CES production function","slug":"ces-production-function","latex":"Y = A\\big[\\alpha K^{\\rho} + (1 - \\alpha) L^{\\rho}\\big]^{1/\\rho}","area":"Growth, trade and environment","about":"Production (or utility) with a constant elasticity of substitution 1/(1 - rho) between inputs.","names":["constant elasticity of substitution","CES production","CES utility","CES function"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Cobb-Douglas production function","slug":"cobb-douglas-production-function","latex":"Y = A\\, K^{\\alpha} L^{1 - \\alpha}","area":"Growth, trade and environment","about":"Output from capital and labour with constant output shares.","names":["Cobb-Douglas"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Cointegration and error correction (VECM)","slug":"cointegration-and-error-correction-vecm","latex":"\\Delta y_t = \\Pi\\, y_{t-1} + \\sum_{i=1}^{p-1}\\Gamma_i\\,\\Delta y_{t-i} + \\varepsilon_t","area":"Time series","about":"Models series that share a long-run equilibrium; Pi holds the cointegrating relations and adjustment speeds.","names":["cointegration","co-integration","error correction model","vector error correction","VECM","Johansen test"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Consumption Euler equation","slug":"consumption-euler-equation","latex":"u'(c_t) = \\beta\\,E_t\\big[(1 + r_{t+1})\\,u'(c_{t+1})\\big]","area":"Macroeconomics","about":"Optimal saving condition: the marginal utility of consuming today equals the discounted expected return of saving it.","names":["Euler equation","consumption Euler"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Contrastive loss (InfoNCE)","slug":"contrastive-loss-infonce","latex":"\\mathcal{L} = -\\log \\frac{\\exp(\\mathrm{sim}(z_i, z_j)/\\tau)}{\\sum_{k \\ne i} \\exp(\\mathrm{sim}(z_i, z_k)/\\tau)}","area":"Machine learning","about":"Pulls representations of matching pairs together and pushes others apart.","names":["InfoNCE","contrastive loss","contrastive learning","NT-Xent"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Convolutional neural network (CNN)","slug":"convolutional-neural-network-cnn","latex":"(I * K)(i, j) = \\sum_{m}\\sum_{n} I(i + m,\\, j + n)\\, K(m, n)","area":"Machine learning","about":"Networks built from learned convolution filters, standard for images and other grid data.","names":["convolutional neural network","CNN","ConvNet"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + U_2},\\quad T = \\alpha U_1 + \\beta U_2,\\quad D = \\sqrt{C\\, T}","area":"Game theory and decision analysis","about":"Measures how well two systems (for example the economy and the environment) develop together.","names":["coupling coordination","coupled coordination"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"CoVaR (systemic risk)","slug":"covar-systemic-risk","latex":"\\Pr\\big(X^{\\mathrm{sys}} \\le \\mathrm{CoVaR}_q^{\\mathrm{sys} \\mid i} \\mid X^{i} = \\mathrm{VaR}_q^{i}\\big) = q","area":"Asset pricing and risk","about":"Value at risk of the financial system conditional on an institution being in distress; Delta CoVaR measures its contribution.","names":["CoVaR","delta CoVaR"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Covered interest parity","slug":"covered-interest-parity","latex":"\\frac{F_t}{S_t} = \\frac{1 + i_t}{1 + i_t^{*}}","area":"Macroeconomics","about":"The forward premium of a currency equals the interest rate differential; deviations signal funding frictions.","names":["covered interest parity","covered interest rate parity","CIP deviation"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Cox proportional hazards model","slug":"cox-proportional-hazards-model","latex":"h(t \\mid x) = h_0(t)\\,\\exp(x^\\top\\beta)","area":"Regression models","about":"Models the hazard of an event over time as a baseline hazard scaled by the regressors.","names":["Cox proportional hazard","proportional hazards model","Cox regression","Cox model","Cox hazard model"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Cross-entropy loss","slug":"cross-entropy-loss","latex":"\\mathcal{L} = -\\sum_{c=1}^{C} y_c \\log \\hat y_c","area":"Machine learning","about":"Standard loss for classification: the negative log-probability of the true class.","names":["cross-entropy"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Dechow-Dichev accruals quality","slug":"dechow-dichev-accruals-quality","latex":"\\Delta WC_{it} = \\beta_0 + \\beta_1\\, CFO_{i,t-1} + \\beta_2\\, CFO_{it} + \\beta_3\\, CFO_{i,t+1} + \\varepsilon_{it}","area":"Accounting","about":"Measures how well working-capital accruals map into past, current and future cash flows.","names":["Dechow and Dichev","Dechow-Dichev","accruals quality","accrual quality"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"DEMATEL","slug":"dematel","latex":"T = X\\,(I - X)^{-1}","area":"Game theory and decision analysis","about":"Maps cause-and-effect relations among factors from a normalized direct-influence matrix X.","names":["DEMATEL"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Denoising diffusion model","slug":"denoising-diffusion-model","latex":"\\mathcal{L} = E_{t, x_0, \\epsilon}\\Big[\\left\\lVert \\epsilon - \\epsilon_\\theta\\big(\\sqrt{\\bar\\alpha_t}\\, x_0 + \\sqrt{1 - \\bar\\alpha_t}\\, \\epsilon,\\ t\\big) \\right\\rVert^2\\Big]","area":"Machine learning","about":"Generative model that learns to remove noise step by step; the basis of current image generators.","names":["denoising diffusion","diffusion probabilistic","latent diffusion","score-based generative","Stable Diffusion"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Difference-in-differences","slug":"difference-in-differences","latex":"Y_{it} = \\alpha_i + \\lambda_t + \\delta\\,(\\mathit{Treat}_i \\times \\mathit{Post}_t) + \\varepsilon_{it}","area":"Causal inference","about":"Compares the change in outcomes of a group exposed to a policy or event with the change in an unexposed group; delta is the estimated effect.","names":["difference-in-difference","differences-in-differences","diff-in-diff","staggered DID","DiD","DID","DDD"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Dividend discount (Gordon growth) model","slug":"dividend-discount-gordon-growth-model","latex":"P_0 = \\frac{D_1}{r - g}","area":"Asset pricing and risk","about":"Values a stock as next year's dividend divided by the discount rate minus the dividend growth rate.","names":["dividend discount model","Gordon growth model"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Entropy weight method","slug":"entropy-weight-method","latex":"e_j = -\\frac{1}{\\ln n}\\sum_{i=1}^{n} p_{ij}\\ln p_{ij},\\quad w_j = \\frac{1 - e_j}{\\sum_k (1 - e_k)}","area":"Game theory and decision analysis","about":"Weights indicators by how much their values vary across units, often to build composite indices.","names":["entropy weight","entropy weighting","entropy method"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Environmental Kuznets curve","slug":"environmental-kuznets-curve","latex":"\\ln E_{it} = \\beta_0 + \\beta_1 \\ln Y_{it} + \\beta_2 (\\ln Y_{it})^2 + \\varepsilon_{it}","area":"Growth, trade and environment","about":"Tests whether pollution first rises and then falls as income grows (beta_2 < 0).","names":["environmental Kuznets curve","Kuznets curve","EKC"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Fama-French five-factor model","slug":"fama-french-five-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + r_i\\,\\mathit{RMW}_t + c_i\\,\\mathit{CMA}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Adds profitability (RMW) and investment (CMA) factors to the three-factor model.","names":["Fama-French five-factor","Fama and French five-factor","Fama-French 5-factor","five-factor model","FF5"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Fama-French three-factor model","slug":"fama-french-three-factor-model","latex":"R_{it} - R_{ft} = \\alpha_i + b_i\\,\\mathit{MKT}_t + s_i\\,\\mathit{SMB}_t + h_i\\,\\mathit{HML}_t + \\varepsilon_{it}","area":"Asset pricing and risk","about":"Explains excess returns with the market, size (SMB) and value (HML) factors.","names":["Fama-French three-factor","Fama and French three-factor","Fama-French 3-factor","Fama and French 3-factor","three-factor model","FF3"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Fisher equation","slug":"fisher-equation","latex":"i_t \\approx r_t + E_t[\\pi_{t+1}]","area":"Macroeconomics","about":"The nominal interest rate equals the real rate plus expected inflation.","names":["Fisher equation","Fisher effect","Fisher hypothesis"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"GARCH","slug":"garch","latex":"\\sigma_t^2 = \\omega + \\alpha\\,\\varepsilon_{t-1}^2 + \\beta\\,\\sigma_{t-1}^2","area":"Time series","about":"Models time-varying volatility: today's variance depends on yesterday's shock and variance (GARCH(1,1)).","names":["GARCH","EGARCH","TGARCH","FIGARCH","MGARCH","generalized autoregressive conditional heteroskedasticity","generalized autoregressive conditional heteroscedasticity"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Gated recurrent unit (GRU)","slug":"gated-recurrent-unit-gru","latex":"h_t = (1 - z_t) \\odot h_{t-1} + z_t \\odot \\tilde h_t","area":"Machine learning","about":"A simpler gated recurrent cell with update and reset gates.","names":["gated recurrent unit","GRU"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Generative adversarial network (GAN)","slug":"generative-adversarial-network-gan","latex":"\\min_G \\max_D\\ E_x\\big[\\log D(x)\\big] + E_z\\big[\\log\\big(1 - D(G(z))\\big)\\big]","area":"Machine learning","about":"A generator and a discriminator trained against each other.","names":["generative adversarial","GAN"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Gradient boosting (XGBoost)","slug":"gradient-boosting-xgboost","latex":"\\mathcal{L} = \\sum_i l(y_i, \\hat y_i) + \\sum_k \\Omega(f_k),\\quad \\Omega(f) = \\gamma T + \\tfrac{1}{2}\\lambda \\lVert w \\rVert^2","area":"Machine learning","about":"Adds trees one at a time, each fitted to the errors of the ensemble so far, with a penalty on tree complexity.","names":["XGBoost","gradient boosting","LightGBM","CatBoost","GBDT"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Granger causality","slug":"granger-causality","latex":"y_t = \\sum_{i=1}^{p} a_i\\, y_{t-i} + \\sum_{j=1}^{p} b_j\\, x_{t-j} + \\varepsilon_t,\\quad H_0: b_1 = \\dots = b_p = 0","area":"Time series","about":"Tests whether past values of x help predict y beyond y's own past.","names":["Granger causality","Granger cause","Granger causal","Granger non-causality"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Graph neural network (graph convolution)","slug":"graph-neural-network-graph-convolution","latex":"H^{(l+1)} = \\sigma\\big(\\tilde D^{-1/2} \\tilde A\\, \\tilde D^{-1/2} H^{(l)} W^{(l)}\\big)","area":"Machine learning","about":"Updates each node's representation from its neighbours' representations.","names":["graph neural network","graph convolutional network","graph convolution","graph attention network","GCN","GNN"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Gravity model of trade","slug":"gravity-model-of-trade","latex":"X_{ij} = G\\,\\frac{Y_i^{\\beta_1}\\, Y_j^{\\beta_2}}{D_{ij}^{\\beta_3}}","area":"Growth, trade and environment","about":"Trade between two countries rises with their economic size and falls with the distance between them.","names":["gravity model","gravity equation","structural gravity","PPML"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Heckman selection model","slug":"heckman-selection-model","latex":"E[y_i \\mid x_i, s_i = 1] = x_i^\\top\\beta + \\rho\\,\\sigma_\\varepsilon\\,\\lambda(z_i^\\top\\gamma),\\quad \\lambda(\\cdot) = \\frac{\\phi(\\cdot)}{\\Phi(\\cdot)}","area":"Causal inference","about":"Corrects for non-random selection of the observed sample with the inverse Mills ratio from a first-stage probit.","names":["Heckman selection","Heckman two-step","Heckman two-stage","Heckman correction","Heckman model","inverse Mills ratio","sample selection model"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Heston stochastic volatility model","slug":"heston-stochastic-volatility-model","latex":"dv_t = \\kappa\\,(\\theta - v_t)\\,dt + \\xi\\sqrt{v_t}\\,dW_t^{v}","area":"Asset pricing and risk","about":"Option pricing model in which the variance follows a mean-reverting square-root process.","names":["Heston model","Heston stochastic volatility","Heston's model"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Hodrick-Prescott filter","slug":"hodrick-prescott-filter","latex":"\\min_{\\{\\tau_t\\}} \\sum_{t=1}^{T}(y_t - \\tau_t)^2 + \\lambda \\sum_{t=2}^{T-1}\\big[(\\tau_{t+1} - \\tau_t) - (\\tau_t - \\tau_{t-1})\\big]^2","area":"Time series","about":"Separates a series into a smooth trend and a cyclical component.","names":["Hodrick-Prescott","HP filter","HP-filtered"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Jensen's alpha","slug":"jensen-s-alpha","latex":"\\alpha_p = R_p - \\big[R_f + \\beta_p\\,(R_m - R_f)\\big]","area":"Asset pricing and risk","about":"A portfolio's return beyond what the CAPM predicts for its beta.","names":["Jensen's alpha","Jensen alpha"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"k-means clustering","slug":"k-means-clustering","latex":"\\min_{C_1, \\dots, C_k} \\sum_{j=1}^{k} \\sum_{x \\in C_j} \\lVert x - \\mu_j \\rVert^2","area":"Machine learning","about":"Partitions observations into k clusters around their means.","names":["k-means"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Kalman filter","slug":"kalman-filter","latex":"\\hat x_{t \\mid t} = \\hat x_{t \\mid t-1} + K_t\\,(y_t - H\\,\\hat x_{t \\mid t-1})","area":"Time series","about":"Recursively updates estimates of an unobserved state from noisy observations.","names":["Kalman filter","Kalman filtering","Kalman smoother"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Kaya identity","slug":"kaya-identity","latex":"\\mathrm{CO_2} = P \\times \\frac{\\mathit{GDP}}{P} \\times \\frac{E}{\\mathit{GDP}} \\times \\frac{\\mathrm{CO_2}}{E}","area":"Growth, trade and environment","about":"Decomposes carbon emissions into population, income per person, energy intensity and carbon intensity.","names":["Kaya identity"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Kullback-Leibler divergence","slug":"kullback-leibler-divergence","latex":"D_{\\mathrm{KL}}(P \\parallel Q) = \\sum_x P(x) \\log \\frac{P(x)}{Q(x)}","area":"Machine learning","about":"How much one probability distribution differs from another.","names":["Kullback-Leibler","KL divergence"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Lerner index","slug":"lerner-index","latex":"L = \\frac{P - MC}{P}","area":"Labour, inequality and competition","about":"Market power as the markup of price over marginal cost.","names":["Lerner index"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Little's law","slug":"little-s-law","latex":"L = \\lambda W","area":"Efficiency and operations","about":"Average number in a queueing system equals the arrival rate times the average time spent in it.","names":["Little's law","Little's formula"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Low-rank adaptation (LoRA)","slug":"low-rank-adaptation-lora","latex":"W = W_0 + B A,\\quad B \\in \\mathbb{R}^{d \\times r},\\ A \\in \\mathbb{R}^{r \\times k},\\ r \\ll \\min(d, k)","area":"Machine learning","about":"Fine-tunes a large model by learning a small low-rank update to its weights.","names":["low-rank adaptation","LoRA"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Merton model (distance to default)","slug":"merton-model-distance-to-default","latex":"DD = \\frac{\\ln(V/D) + (\\mu - \\sigma_V^2/2)\\,T}{\\sigma_V\\sqrt{T}}","area":"Asset pricing and risk","about":"Treats equity as a call option on firm assets V; distance to default measures how far assets are from the default point D.","names":["distance to default","Merton model","Merton's model","KMV"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Mincer earnings equation","slug":"mincer-earnings-equation","latex":"\\ln w_i = \\beta_0 + \\beta_1 S_i + \\beta_2 X_i + \\beta_3 X_i^2 + \\varepsilon_i","area":"Labour, inequality and competition","about":"Log wages as a function of years of schooling S and experience X.","names":["Mincer equation","Mincer earnings","Mincerian","Mincer wage","Mincer-type"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Modified Jones model (discretionary accruals)","slug":"modified-jones-model-discretionary-accruals","latex":"\\frac{TA_{it}}{A_{i,t-1}} = \\alpha_1\\frac{1}{A_{i,t-1}} + \\alpha_2\\frac{\\Delta REV_{it} - \\Delta REC_{it}}{A_{i,t-1}} + \\alpha_3\\frac{PPE_{it}}{A_{i,t-1}} + \\varepsilon_{it}","area":"Accounting","about":"Separates total accruals into normal and discretionary parts; the residual is used as a measure of earnings management.","names":["modified Jones","Jones model","Jones (1991)","discretionary accrual"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Nash bargaining solution","slug":"nash-bargaining-solution","latex":"\\max_{x}\\ \\big(u_1(x) - d_1\\big)\\big(u_2(x) - d_2\\big)","area":"Game theory and decision analysis","about":"Splits a surplus by maximizing the product of the parties' gains over their disagreement points.","names":["Nash bargaining"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Nelson-Siegel yield curve","slug":"nelson-siegel-yield-curve","latex":"y(\\tau) = \\beta_0 + \\beta_1\\frac{1 - e^{-\\tau/\\lambda}}{\\tau/\\lambda} + \\beta_2\\Big(\\frac{1 - e^{-\\tau/\\lambda}}{\\tau/\\lambda} - e^{-\\tau/\\lambda}\\Big)","area":"Asset pricing and risk","about":"Fits the term structure of interest rates with level, slope and curvature factors.","names":["Nelson-Siegel"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"New Keynesian Phillips curve","slug":"new-keynesian-phillips-curve","latex":"\\pi_t = \\beta\\,E_t[\\pi_{t+1}] + \\kappa\\, x_t","area":"Macroeconomics","about":"Links inflation to expected future inflation and the output gap (or real marginal cost) x.","names":["Phillips curve"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Okun's law","slug":"okun-s-law","latex":"\\Delta u_t = -\\beta\\,(g_t - \\bar g)","area":"Macroeconomics","about":"Links changes in unemployment to output growth relative to its trend.","names":["Okun's law","Okun law"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Principal component analysis (PCA)","slug":"principal-component-analysis-pca","latex":"\\max_{\\lVert w \\rVert = 1}\\ w^\\top \\Sigma\\, w","area":"Machine learning","about":"Finds the orthogonal directions of largest variance in the data.","names":["principal component analysis","principal components analysis","PCA"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Probit model","slug":"probit-model","latex":"\\Pr(y = 1 \\mid x) = \\Phi(x^\\top\\beta)","area":"Regression models","about":"Models the probability of a binary outcome with the standard normal distribution function.","names":["probit"],"papers":0,"papers_7d":0,"page":false},{"rank":33,"name":"Propensity score matching","slug":"propensity-score-matching","latex":"e(x) = \\Pr(D = 1 \\mid X = x)","area":"Causal inference","about":"Matches treated and untreated units with 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(XGBoost)","slug":"gradient-boosting-xgboost","latex":"\\mathcal{L} = \\sum_i l(y_i, \\hat y_i) + \\sum_k \\Omega(f_k),\\quad \\Omega(f) = \\gamma T + \\tfrac{1}{2}\\lambda \\lVert w \\rVert^2","area":"Machine learning","about":"Adds trees one at a time, each fitted to the errors of the ensemble so far, with a penalty on tree complexity.","names":["XGBoost","gradient boosting","LightGBM","CatBoost","GBDT"],"papers":10,"papers_7d":1,"page":true},{"rank":7,"name":"Shapley value (SHAP)","slug":"shapley-value-shap","latex":"\\phi_i(v) = \\sum_{S \\subseteq N \\setminus \\{i\\}} \\frac{\\lvert S \\rvert!\\,(n - \\lvert S \\rvert - 1)!}{n!}\\big[v(S \\cup \\{i\\}) - v(S)\\big]","area":"Game theory and decision analysis","about":"A player's average marginal contribution over all coalitions; SHAP uses it to explain machine-learning predictions.","names":["Shapley value","SHAP","Shapley additive explanation"],"papers":10,"papers_7d":0,"page":true},{"rank":9,"name":"Random 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and differencing order d.","names":["ARIMA","SARIMA","ARMA","ARFIMA","autoregressive integrated moving average","autoregressive moving average"],"papers":7,"papers_7d":1,"page":true},{"rank":11,"name":"Q-learning","slug":"q-learning","latex":"Q(s, a) \\leftarrow Q(s, a) + \\alpha\\big[r + \\gamma \\max_{a'} Q(s', a') - Q(s, a)\\big]","area":"Machine learning","about":"Reinforcement learning of action values from rewards; deep Q-networks approximate Q with a neural network.","names":["Q-learning","deep Q-network","DQN"],"papers":7,"papers_7d":1,"page":true},{"rank":13,"name":"Denoising diffusion model","slug":"denoising-diffusion-model","latex":"\\mathcal{L} = E_{t, x_0, \\epsilon}\\Big[\\left\\lVert \\epsilon - \\epsilon_\\theta\\big(\\sqrt{\\bar\\alpha_t}\\, x_0 + \\sqrt{1 - \\bar\\alpha_t}\\, \\epsilon,\\ t\\big) \\right\\rVert^2\\Big]","area":"Machine learning","about":"Generative model that learns to remove noise step by step; the basis of current image generators.","names":["denoising diffusion","diffusion probabilistic","latent diffusion","score-based generative","Stable Diffusion"],"papers":6,"papers_7d":0,"page":true},{"rank":13,"name":"LASSO","slug":"lasso","latex":"\\hat\\beta = \\operatorname*{arg\\,min}_{\\beta}\\ \\lVert y - X\\beta \\rVert_2^2 + \\lambda \\lVert \\beta \\rVert_1","area":"Regression models","about":"Regression with an L1 penalty that shrinks coefficients and sets many of them to exactly zero.","names":["Lasso","least absolute shrinkage"],"papers":6,"papers_7d":0,"page":true},{"rank":13,"name":"Low-rank adaptation (LoRA)","slug":"low-rank-adaptation-lora","latex":"W = W_0 + B A,\\quad B \\in \\mathbb{R}^{d \\times r},\\ A \\in \\mathbb{R}^{r \\times k},\\ r \\ll \\min(d, k)","area":"Machine learning","about":"Fine-tunes a large model by learning a small low-rank update to its weights.","names":["low-rank adaptation","LoRA"],"papers":6,"papers_7d":0,"page":true},{"rank":16,"name":"Gated recurrent unit (GRU)","slug":"gated-recurrent-unit-gru","latex":"h_t = (1 - z_t) \\odot h_{t-1} + z_t \\odot \\tilde h_t","area":"Machine learning","about":"A simpler gated recurrent cell with update and reset gates.","names":["gated recurrent unit","GRU"],"papers":5,"papers_7d":0,"page":true},{"rank":16,"name":"Variational autoencoder (ELBO)","slug":"variational-autoencoder-elbo","latex":"\\log p_\\theta(x) \\ge E_{q_\\phi(z \\mid x)}\\big[\\log p_\\theta(x \\mid z)\\big] - D_{\\mathrm{KL}}\\big(q_\\phi(z \\mid x) \\parallel p(z)\\big)","area":"Machine learning","about":"Generative model trained by maximizing the evidence lower bound on the data likelihood.","names":["variational autoencoder","variational auto-encoder","evidence lower bound","ELBO","VAE"],"papers":5,"papers_7d":1,"page":true},{"rank":18,"name":"Generative adversarial network (GAN)","slug":"generative-adversarial-network-gan","latex":"\\min_G \\max_D\\ E_x\\big[\\log D(x)\\big] + E_z\\big[\\log\\big(1 - D(G(z))\\big)\\big]","area":"Machine learning","about":"A generator and a discriminator trained against each other.","names":["generative adversarial","GAN"],"papers":4,"papers_7d":0,"page":true},{"rank":18,"name":"Gradient descent","slug":"gradient-descent","latex":"\\theta_{t+1} = \\theta_t - \\eta\\, \\nabla_\\theta \\mathcal{L}(\\theta_t)","area":"Machine learning","about":"Moves parameters a step against the gradient of the loss; stochastic gradient descent uses mini-batches.","names":["gradient descent","SGD"],"papers":4,"papers_7d":1,"page":true},{"rank":18,"name":"k-means clustering","slug":"k-means-clustering","latex":"\\min_{C_1, \\dots, C_k} \\sum_{j=1}^{k} \\sum_{x \\in C_j} \\lVert x - \\mu_j \\rVert^2","area":"Machine learning","about":"Partitions observations into k clusters around their means.","names":["k-means"],"papers":4,"papers_7d":1,"page":true},{"rank":18,"name":"Kalman filter","slug":"kalman-filter","latex":"\\hat x_{t \\mid t} = \\hat x_{t \\mid t-1} + K_t\\,(y_t - H\\,\\hat x_{t \\mid t-1})","area":"Time series","about":"Recursively updates estimates of an unobserved state from noisy observations.","names":["Kalman filter","Kalman filtering","Kalman smoother"],"papers":4,"papers_7d":0,"page":true},{"rank":18,"name":"Kullback-Leibler divergence","slug":"kullback-leibler-divergence","latex":"D_{\\mathrm{KL}}(P \\parallel Q) = \\sum_x P(x) \\log \\frac{P(x)}{Q(x)}","area":"Machine learning","about":"How much one probability distribution differs from another.","names":["Kullback-Leibler","KL divergence"],"papers":4,"papers_7d":0,"page":true},{"rank":23,"name":"Analytic hierarchy process (AHP)","slug":"analytic-hierarchy-process-ahp","latex":"A\\, w = \\lambda_{\\max}\\, w,\\quad CR = \\frac{(\\lambda_{\\max} - n)/(n - 1)}{RI}","area":"Game theory and decision analysis","about":"Derives criteria weights from pairwise comparisons; CR checks their consistency.","names":["analytic hierarchy process","analytical hierarchy process","AHP"],"papers":3,"papers_7d":0,"page":true},{"rank":23,"name":"Linear and integer programming","slug":"linear-and-integer-programming","latex":"\\min_{x}\\ c^\\top x\\ \\ \\text{s.t.}\\ \\ A x \\le b,\\ x \\ge 0,\\ x_j \\in \\mathbb{Z}\\ (j \\in I)","area":"Efficiency and operations","about":"Optimizes a linear objective under linear constraints, with some variables restricted to integers.","names":["linear programming","linear program","integer programming","integer program","MILP","MINLP","mixed-integer"],"papers":3,"papers_7d":0,"page":true},{"rank":23,"name":"Quantile regression","slug":"quantile-regression","latex":"\\hat\\beta_\\tau = \\operatorname*{arg\\,min}_{\\beta} \\sum_{i} \\rho_\\tau(y_i - x_i^\\top\\beta),\\quad \\rho_\\tau(u) = u\\,(\\tau - \\mathbf{1}\\{u < 0\\})","area":"Regression models","about":"Estimates how regressors shift a chosen quantile of the outcome rather than its mean.","names":["quantile regression","quantile-on-quantile"],"papers":3,"papers_7d":0,"page":true},{"rank":23,"name":"Structural equation modeling (SEM)","slug":"structural-equation-modeling-sem","latex":"\\eta = B\\eta + \\Gamma\\xi + \\zeta,\\quad y = \\Lambda_y\\,\\eta + \\varepsilon","area":"Regression models","about":"Estimates relations among latent constructs measured by several observed indicators; PLS-SEM is a common variant.","names":["structural equation model","structural equation modeling","structural equation modelling","PLS-SEM","partial least squares structural equation","CB-SEM"],"papers":3,"papers_7d":0,"page":true},{"rank":27,"name":"Data envelopment analysis (DEA)","slug":"data-envelopment-analysis-dea","latex":"\\max_{u, v}\\ \\frac{\\sum_r u_r\\, y_{r0}}{\\sum_i v_i\\, x_{i0}}\\ \\ \\text{s.t.}\\ \\ \\frac{\\sum_r u_r\\, y_{rj}}{\\sum_i v_i\\, x_{ij}} \\le 1\\ \\ \\forall j","area":"Efficiency and operations","about":"Scores the efficiency of each unit as its best ratio of weighted outputs to weighted inputs relative to all units.","names":["data envelopment analysis","DEA model","super-efficiency DEA","slacks-based measure","SBM model","network DEA","DEA"],"papers":2,"papers_7d":0,"page":true},{"rank":27,"name":"Expected shortfall (CVaR)","slug":"expected-shortfall-cvar","latex":"\\mathrm{ES}_\\alpha(L) = \\frac{1}{1 - \\alpha}\\int_\\alpha^{1} \\mathrm{VaR}_u(L)\\,du","area":"Asset pricing and risk","about":"Average loss in the worst 1 - alpha share of outcomes; also called conditional value at risk.","names":["expected shortfall","conditional value at risk","CVaR"],"papers":2,"papers_7d":0,"page":true},{"rank":27,"name":"Granger causality","slug":"granger-causality","latex":"y_t = \\sum_{i=1}^{p} a_i\\, y_{t-i} + \\sum_{j=1}^{p} b_j\\, x_{t-j} + \\varepsilon_t,\\quad H_0: b_1 = \\dots = b_p = 0","area":"Time series","about":"Tests whether past values of x help predict y beyond y's own past.","names":["Granger causality","Granger cause","Granger 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\\epsilon)\\,\\hat A_t\\big)\\big]","area":"Machine learning","about":"Policy-gradient reinforcement learning with a clipped objective that keeps updates small.","names":["proximal policy optimization","proximal policy optimisation","PPO"],"papers":2,"papers_7d":0,"page":true},{"rank":27,"name":"Sharpe ratio","slug":"sharpe-ratio","latex":"S_p = \\frac{E[R_p] - R_f}{\\sigma_p}","area":"Asset pricing and risk","about":"Excess return of a portfolio per unit of total risk.","names":["Sharpe ratio"],"papers":2,"papers_7d":0,"page":true},{"rank":27,"name":"Softmax function","slug":"softmax-function","latex":"\\mathrm{softmax}(z)_i = \\frac{e^{z_i}}{\\sum_{j=1}^{K} e^{z_j}}","area":"Machine learning","about":"Turns a vector of scores into probabilities.","names":["softmax"],"papers":2,"papers_7d":0,"page":true},{"rank":27,"name":"TOPSIS","slug":"topsis","latex":"C_i = \\frac{d_i^{-}}{d_i^{+} + d_i^{-}}","area":"Game theory and decision analysis","about":"Ranks alternatives by closeness to the ideal solution and distance from the worst one.","names":["TOPSIS"],"papers":2,"papers_7d":1,"page":true},{"rank":27,"name":"Value at risk (VaR)","slug":"value-at-risk-var","latex":"\\mathrm{VaR}_\\alpha(L) = \\inf\\{\\ell \\in \\mathbb{R} : \\Pr(L > \\ell) \\le 1 - \\alpha\\}","area":"Asset pricing and risk","about":"The loss that is exceeded with probability at most 1 - alpha over a given horizon.","names":["value at risk","VaR"],"papers":2,"papers_7d":0,"page":true},{"rank":37,"name":"Best-worst method","slug":"best-worst-method","latex":"\\min\\ \\xi\\ \\ \\text{s.t.}\\ \\ \\lvert w_B - a_{Bj}\\, w_j \\rvert \\le \\xi,\\ \\ \\lvert w_j - a_{jW}\\, w_W \\rvert \\le \\xi,\\ \\ \\sum_j w_j = 1","area":"Game theory and decision analysis","about":"Derives criteria weights from comparisons with the best and the worst criterion.","names":["best-worst method","BWM"],"papers":1,"papers_7d":0,"page":true},{"rank":37,"name":"Cross-entropy 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effect.","names":["difference-in-difference","differences-in-differences","diff-in-diff","staggered DID","DiD","DID","DDD"],"papers":1,"papers_7d":0,"page":true},{"rank":37,"name":"Entropy weight method","slug":"entropy-weight-method","latex":"e_j = -\\frac{1}{\\ln n}\\sum_{i=1}^{n} p_{ij}\\ln p_{ij},\\quad w_j = \\frac{1 - e_j}{\\sum_k (1 - e_k)}","area":"Game theory and decision analysis","about":"Weights indicators by how much their values vary across units, often to build composite indices.","names":["entropy weight","entropy weighting","entropy method"],"papers":1,"papers_7d":1,"page":true},{"rank":37,"name":"GARCH","slug":"garch","latex":"\\sigma_t^2 = \\omega + \\alpha\\,\\varepsilon_{t-1}^2 + \\beta\\,\\sigma_{t-1}^2","area":"Time series","about":"Models time-varying volatility: today's variance depends on yesterday's shock and variance (GARCH(1,1)).","names":["GARCH","EGARCH","TGARCH","FIGARCH","MGARCH","generalized autoregressive conditional heteroskedasticity","generalized 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1 \\mid X = x)","area":"Causal inference","about":"Matches treated and untreated units with similar probabilities of treatment given their characteristics.","names":["propensity score","PSM"],"papers":1,"papers_7d":0,"page":true},{"rank":37,"name":"Regression discontinuity design","slug":"regression-discontinuity-design","latex":"\\tau = \\lim_{x \\downarrow c} E[Y \\mid X = x] - \\lim_{x \\uparrow c} E[Y \\mid X = x]","area":"Causal inference","about":"Estimates an effect from the jump in outcomes at a cutoff c of a running variable X that decides treatment.","names":["regression discontinuity","RDD"],"papers":1,"papers_7d":0,"page":true},{"rank":37,"name":"Shannon entropy","slug":"shannon-entropy","latex":"H(X) = -\\sum_x p(x) \\log p(x)","area":"Machine learning","about":"The average information content, or uncertainty, of a random variable.","names":["Shannon entropy","information entropy"],"papers":1,"papers_7d":0,"page":true},{"rank":37,"name":"Two-way fixed-effects panel 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v_t} + \\epsilon}","area":"Machine learning","about":"Gradient descent with running averages of the gradient (m) and its square (v).","names":["Adam optimizer","Adam optimiser","Adam optimization","Adam algorithm","AdamW"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Altman Z-score","slug":"altman-z-score","latex":"Z = 1.2X_1 + 1.4X_2 + 3.3X_3 + 0.6X_4 + 1.0X_5","area":"Asset pricing and risk","about":"Bankruptcy predictor that weights five accounting ratios (working capital, retained earnings, EBIT, market equity, sales).","names":["Altman Z","Altman's Z"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Amihud illiquidity ratio","slug":"amihud-illiquidity-ratio","latex":"\\mathit{ILLIQ}_i = \\frac{1}{D_i}\\sum_{d=1}^{D_i}\\frac{\\lvert R_{id} \\rvert}{\\mathit{DVOL}_{id}}","area":"Asset pricing and risk","about":"Average absolute daily return per dollar of trading volume: the price impact of trading.","names":["Amihud illiquidity","Amihud's illiquidity","Amihud measure","Amihud's measure","Amihud ratio"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Autoregressive distributed lag (ARDL)","slug":"autoregressive-distributed-lag-ardl","latex":"y_t = \\alpha + \\sum_{i=1}^{p}\\phi_i\\, y_{t-i} + \\sum_{j=0}^{q}\\beta_j^\\top x_{t-j} + \\varepsilon_t","area":"Time series","about":"Regresses a series on its own lags and current and lagged regressors; the bounds test checks for a long-run relation.","names":["autoregressive distributed lag","ARDL","NARDL","QARDL","CS-ARDL"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Bass diffusion model","slug":"bass-diffusion-model","latex":"\\frac{f(t)}{1 - F(t)} = p + q\\, F(t)","area":"Efficiency and operations","about":"Adoption of a new product driven by innovation (p) and imitation (q).","names":["Bass diffusion","Bass model"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Basu asymmetric timeliness","slug":"basu-asymmetric-timeliness","latex":"\\frac{EPS_{it}}{P_{i,t-1}} = \\beta_0 + \\beta_1 D_{it} + \\beta_2 R_{it} + \\beta_3 D_{it} R_{it} + \\varepsilon_{it}","area":"Accounting","about":"Measures accounting conservatism as how much faster earnings reflect bad news (negative returns) than good news.","names":["asymmetric timeliness","Basu model","Basu (1997)","Basu's model"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Bayes' theorem","slug":"bayes-theorem","latex":"P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}","area":"Game theory and decision analysis","about":"Updates the probability of a hypothesis A after observing evidence B.","names":["Bayes' theorem","Bayes theorem","Bayes' rule","Bayes rule","Bayesian updating"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Bellman equation","slug":"bellman-equation","latex":"V(s) = \\max_{a}\\left\\{ r(s, a) + \\beta \\sum_{s'} P(s' \\mid s, a)\\, V(s') \\right\\}","area":"Game theory and decision analysis","about":"Recursive condition for the value of a dynamic optimization or Markov decision problem.","names":["Bellman equation","Hamilton-Jacobi-Bellman","HJB equation","Bellman optimality"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Beneish M-score","slug":"beneish-m-score","latex":"M = -4.84 + 0.92\\,\\mathit{DSRI} + 0.528\\,\\mathit{GMI} + 0.404\\,\\mathit{AQI} + 0.892\\,\\mathit{SGI} + 0.115\\,\\mathit{DEPI} - 0.172\\,\\mathit{SGAI} + 4.679\\,\\mathit{TATA} - 0.327\\,\\mathit{LVGI}","area":"Accounting","about":"Flags likely earnings manipulation from eight financial-statement ratios.","names":["Beneish M-score","Beneish model","Beneish's M-score","M-score"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Black-Scholes formula","slug":"black-scholes-formula","latex":"C = S_0\\,N(d_1) - K e^{-rT} N(d_2),\\quad d_{1,2} = \\frac{\\ln(S_0/K) + (r \\pm \\sigma^2/2)\\,T}{\\sigma\\sqrt{T}}","area":"Asset pricing and risk","about":"Price of a European call option on a stock with constant volatility and interest 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long-run equilibrium; Pi holds the cointegrating relations and adjustment speeds.","names":["cointegration","co-integration","error correction model","vector error correction","VECM","Johansen test"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Consumption Euler equation","slug":"consumption-euler-equation","latex":"u'(c_t) = \\beta\\,E_t\\big[(1 + r_{t+1})\\,u'(c_{t+1})\\big]","area":"Macroeconomics","about":"Optimal saving condition: the marginal utility of consuming today equals the discounted expected return of saving it.","names":["Euler equation","consumption Euler"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Coupling coordination degree","slug":"coupling-coordination-degree","latex":"C = \\frac{2\\sqrt{U_1 U_2}}{U_1 + U_2},\\quad T = \\alpha U_1 + \\beta U_2,\\quad D = \\sqrt{C\\, T}","area":"Game theory and decision analysis","about":"Measures how well two systems (for example the economy and the environment) develop together.","names":["coupling 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\\bar g(\\theta),\\quad \\bar g(\\theta) = \\frac{1}{n}\\sum_{i=1}^{n} g(w_i, \\theta)","area":"Regression models","about":"Estimates parameters by making sample moment conditions as close to zero as possible; system and difference GMM are common in dynamic panels.","names":["generalized method of moments","generalised method of moments","system GMM","difference GMM","GMM estimator","GMM estimation","two-step GMM","Arellano-Bond"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Gravity model of trade","slug":"gravity-model-of-trade","latex":"X_{ij} = G\\,\\frac{Y_i^{\\beta_1}\\, Y_j^{\\beta_2}}{D_{ij}^{\\beta_3}}","area":"Growth, trade and environment","about":"Trade between two countries rises with their economic size and falls with the distance between them.","names":["gravity model","gravity equation","structural gravity","PPML"],"papers":0,"papers_7d":0,"page":false},{"rank":52,"name":"Heckman selection model","slug":"heckman-selection-model","latex":"E[y_i \\mid x_i, s_i 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attribution; commercial use needs permission. The underlying bibliographic records come from OpenAlex (CC0)."}}