Statistics — Page 49
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Time-varying parameter ADF unit root test
The time-varying parameter ADF (TVP-ADF) test extends the classical Augmented Dickey-Fuller framework by allowing the autoregressive coefficient to evolve over time. Rather than assuming a single fixed unit-root parameter throughout the sam...
Time-varying parameter AR model
The Time-Varying Parameter Autoregressive (TVP-AR) model extends the classical AR model by allowing its autoregressive coefficients to drift over time, typically as a random walk. Cast as a state-space system, the model captures gradual str...
Time-varying parameter ARCH model
The Time-Varying Parameter ARCH (TVP-ARCH) model extends the classic ARCH framework by allowing both the conditional mean coefficients and the ARCH variance parameters to drift over time according to a random-walk or state-space process. Th...
Time-varying parameter ARDL bounds test
The time-varying parameter ARDL bounds test extends the classic Pesaran-Shin-Smith (2001) bounds testing framework by allowing regression coefficients to evolve continuously over time. It detects whether a long-run cointegrating relationshi...
Time-varying parameter ARIMA model
The time-varying parameter ARIMA model extends the classical ARIMA framework by allowing its autoregressive and moving-average coefficients to evolve over time rather than remaining fixed. Cast in state-space form and estimated via the Kalm...
Time-varying parameter ARMA model
The time-varying parameter ARMA (TVP-ARMA) model extends the classical ARMA framework by allowing the autoregressive and moving-average coefficients to evolve over time. Embedded in a state-space representation and estimated via the Kalman...
Time-varying parameter Arellano-Bond GMM
The time-varying parameter Arellano-Bond GMM (TVP-AB GMM) is a dynamic panel estimator that extends the classic Arellano-Bond difference GMM framework by allowing regression coefficients to evolve over time. It addresses both individual fix...
Time-varying parameter DCC-GARCH model
The TVP-DCC-GARCH model extends the Dynamic Conditional Correlation GARCH framework by allowing not only the pairwise correlations but also the underlying model parameters to evolve continuously over time. It captures structural shifts in v...
Time-varying parameter EGARCH model
The TVP-EGARCH model extends Nelson's (1991) Exponential GARCH by allowing the volatility equation's parameters — including the leverage effect coefficient — to drift continuously over time. This makes it possible to capture structural chan...
Time-varying parameter Engle-Granger cointegration
Time-varying parameter (TVP) Engle-Granger cointegration extends the classical two-step Engle-Granger framework by allowing the long-run relationship between integrated series to evolve over time. Instead of assuming a fixed cointegrating v...
Time-varying parameter GARCH model
The Time-Varying Parameter GARCH model extends the standard GARCH framework by allowing the conditional variance parameters — including the ARCH and GARCH coefficients — to change over time rather than remaining fixed throughout the sample....
Time-varying parameter GLS
Time-varying parameter GLS extends generalized least squares to settings where regression coefficients are not fixed constants but evolve over time according to a stochastic process. By embedding the model in a state-space framework and app...
Time-varying parameter Granger causality
Time-varying parameter Granger causality extends the classical Granger causality framework by allowing the predictive relationships between time series to evolve across time. Instead of assuming fixed causal effects, the model estimates cau...
Time-varying parameter Hausman test
The time-varying parameter Hausman test extends Hausman's (1978) classic specification test to models whose coefficients are allowed to evolve over time. It compares an efficient estimator (e.g., OLS or GLS assuming constant parameters) wit...
Time-varying parameter Johansen cointegration
Time-varying parameter (TVP) Johansen cointegration extends the classic Johansen framework by allowing the cointegrating vectors and adjustment speeds to evolve over time. It is designed for integrated multivariate time series whose long-ru...
Time-varying parameter KPSS test
The time-varying parameter KPSS test extends the classic Kwiatkowski-Phillips-Schmidt-Shin (1992) stationarity test to settings where the deterministic or stochastic components of a series may shift over time. It tests the null hypothesis o...
Time-varying parameter MA model
The time-varying parameter moving average (TVP-MA) model extends the standard MA model by allowing the moving-average coefficients to change over time. Cast as a state-space system, it is estimated via the Kalman filter and smoother, making...
Time-varying parameter NARDL
The Time-Varying Parameter NARDL (TVP-NARDL) model extends the Nonlinear ARDL framework by allowing the coefficients on positive and negative partial sums of a regressor to change over time. This combination captures both asymmetric respons...
Time-varying parameter OLS
Time-Varying Parameter OLS extends classical ordinary least squares to allow regression coefficients to change over time. Instead of assuming fixed slopes throughout the sample, the model treats each coefficient as a stochastic process, tra...
Time-varying parameter PP unit root test
The time-varying parameter PP unit root test extends the classical Phillips-Perron test by allowing the autoregressive coefficient to change over time. It detects stochastic non-stationarity in series whose persistence may shift across regi...
Time-varying parameter SARIMA model
The Time-Varying Parameter SARIMA model extends the classical SARIMA framework by allowing autoregressive and moving-average coefficients to evolve over time. Cast as a state-space system and estimated with the Kalman filter, it captures bo...
Time-varying parameter SVAR model
The Time-Varying Parameter Structural VAR (TVP-SVAR) model extends classical structural VARs by allowing both the reduced-form coefficients and the structural impact matrix to evolve continuously over time. Estimated via Bayesian MCMC, it c...
Time-varying parameter TGARCH model
The TVP-TGARCH model extends Threshold GARCH by allowing its volatility parameters to evolve over time via a state-space representation. It captures both the leverage effect — that negative return shocks increase volatility more than positi...
Time-varying parameter Toda-Yamamoto causality
The TVP Toda-Yamamoto causality test combines Toda and Yamamoto's (1995) augmented VAR approach — which handles possibly integrated or cointegrated series without pre-testing for unit roots — with time-varying parameters, allowing causal re...