Statistics — Page 32
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Panel ARIMA model
The Panel ARIMA model extends the classical Box-Jenkins ARIMA framework to panel data, fitting autoregressive integrated moving-average dynamics to multiple cross-sectional units observed over time. It accommodates unit-specific short-run d...
Panel ARMA model
The Panel ARMA model extends the classical Autoregressive Moving Average (ARMA) framework to panel data, allowing each cross-sectional unit to carry an individual effect while the within-unit error dynamics follow an ARMA(p, q) process. It...
Panel Arellano-Bond GMM
The Arellano-Bond GMM estimator addresses the two core problems of dynamic panel models — individual fixed effects correlated with the regressors, and the endogeneity introduced by a lagged dependent variable — by first-differencing to remo...
Panel Cointegration Tests
Panel cointegration tests check whether a set of integrated variables share a stable long-run equilibrium relationship across a panel of cross-sectional units. Pedroni (1999, 2004) provides heterogeneous-panel tests with seven statistics, K...
Panel DCC-GARCH
The Panel DCC-GARCH model extends Engle's (2002) Dynamic Conditional Correlation GARCH framework to panel data settings, jointly modelling time-varying volatility and cross-sectional correlations across multiple units (countries, firms, or...
Panel DF-GLS
Panel DF-GLS extends the Elliott, Rothenberg, and Stock (1996) GLS unit-root test to panel data, combining cross-sectional and time-series information to test whether variables contain unit roots. Introduced by Hadri and colleagues (2005),...
Panel Data Analysis
Panel data analysis models data that track multiple units — countries, firms, individuals — over time, enabling researchers to control for unobserved unit-level heterogeneity that would otherwise bias cross-sectional or time-series estimate...
Panel Data Placebo Test
A panel data placebo test is a falsification procedure used to assess the credibility of causal estimates in quasi-experimental panel designs. By applying the same estimation strategy to a period, group, or outcome where no true effect shou...
Panel Dynamic Panel Data Model
The dynamic panel data model extends standard panel regression by including one or more lagged values of the outcome variable as regressors. Because past outcomes directly predict current outcomes, the model captures persistence and adjustm...
Panel EGARCH
Panel EGARCH extends Nelson's (1991) Exponential GARCH model to a panel setting, allowing conditional variance to evolve asymmetrically over time for each cross-sectional unit. The log specification ensures non-negative variance without par...
Panel Engle-Granger Cointegration
The Panel Engle-Granger cointegration test extends the classic two-step Engle-Granger procedure to panel data, allowing researchers to detect long-run equilibrium relationships among integrated variables across multiple cross-sectional unit...
Panel Fixed Effects
The Panel Data Fixed Effects model estimates relationships from panel data (the same units observed over several time periods) while controlling for unit- and/or time-specific effects, supporting causal inference. It is developed as the wit...
Panel Fixed Effects Model
The panel fixed effects (FE) model controls for all time-invariant, unit-specific unobserved heterogeneity by absorbing it into individual intercepts. By sweeping out unit means through the within transformation, FE yields unbiased estimate...
Panel GARCH model
The Panel GARCH model extends Bollerslev's (1986) Generalized Autoregressive Conditional Heteroscedasticity framework to panel data, allowing conditional variance to evolve over time for each cross-sectional unit. It simultaneously captures...
Panel GLS
Panel GLS is a regression method for longitudinal data that explicitly models the non-spherical error structure — heteroscedasticity across units and serial correlation within units — to recover efficient coefficient estimates. Unlike OLS,...
Panel Geary's C
Panel Geary's C extends the classic Geary contiguity ratio to panel datasets, measuring spatial autocorrelation across georeferenced units (regions, cities, countries) observed over multiple time periods. It detects whether neighboring unit...
Panel Geographically Weighted Regression
Panel Geographically Weighted Regression (Panel GWR) extends the standard GWR framework to panel data, allowing regression coefficients to vary both across geographic locations and over time. It captures spatially non-stationary relationshi...
Panel Granger Causality
The Panel Granger Causality test examines whether past values of one variable help predict another variable across multiple cross-sectional units observed over time. It extends the classical Granger causality framework to panel data, accoun...
Panel Hausman Test
The Hausman specification test for panel data determines whether individual-specific effects are correlated with the regressors — a correlation that would make the random effects estimator inconsistent. A statistically significant result fa...
Panel Hot Spot Analysis
Panel Hot Spot Analysis applies hot spot detection — typically via the Getis-Ord Gi* statistic — repeatedly across multiple time periods on the same spatial units, enabling researchers to track where clusters of high or low values persist,...
Panel Johansen Cointegration
The Panel Johansen cointegration test extends Johansen's maximum-likelihood framework to panel data, allowing researchers to test whether multiple non-stationary variables share long-run equilibrium relationships across cross-sectional unit...
Panel KPSS test
The Panel KPSS test, introduced by Hadri (2000), tests the null hypothesis that all series in a panel are stationary against the alternative that some or all contain a unit root. It extends the univariate KPSS framework to panel data by agg...
Panel KSS
The Panel KSS test reverses the null hypothesis of unit-root tests: it tests whether variables are stationary (stationarity is the null) versus nonstationary (unit root is the alternative). Introduced by Kwiatkowski et al. (1992) and extend...
Panel Kernel Density Estimation
Panel Kernel Density Estimation (Panel KDE) extends the standard kernel density estimator to panel (longitudinal) data, estimating smooth density surfaces for spatial or attribute variables observed across multiple units and time periods. I...