Statistics — Page 17
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Fourier Fixed Effects Model
The Fourier fixed effects model extends standard panel fixed effects regression by augmenting the specification with low-frequency Fourier (trigonometric) terms. These sine and cosine components approximate unknown, smooth structural shifts...
Fourier GARCH Model
The Fourier GARCH model embeds trigonometric Fourier terms into a standard GARCH framework to capture smooth, gradual shifts in the conditional variance process without requiring knowledge of exact structural break dates. By approximating u...
Fourier GLS
Fourier GLS embeds low-frequency trigonometric (Fourier) terms into a generalized least squares framework to capture smooth, gradual structural change in a time series without requiring the researcher to specify when or how many breaks occu...
Fourier Granger Causality
The Fourier Granger causality test extends the classic Granger causality framework by embedding low-frequency Fourier terms in the VAR equation, allowing the causal relationship to shift gradually over time without requiring the researcher...
Fourier Hausman test
The Fourier Hausman test extends the classical Hausman endogeneity test by augmenting the regression with Fourier trigonometric terms — sines and cosines of time — so that the test remains valid even when the data-generating process contain...
Fourier Johansen cointegration
The Fourier Johansen cointegration test extends the classical Johansen trace and maximum-eigenvalue tests by embedding low-frequency Fourier terms in the deterministic component of the VECM. This allows the test to remain valid when cointeg...
Fourier KPSS test
The Fourier KPSS test extends the standard KPSS stationarity test by embedding a flexible Fourier series in the deterministic component of the model. This approach captures smooth, gradual structural breaks in the level or trend of a time s...
Fourier MA Model
The Fourier MA model combines a Moving Average (MA) error structure with Fourier series terms — sine and cosine pairs — to capture complex or high-frequency seasonal patterns in time series data. It is particularly useful when the seasonal...
Fourier NARDL
Fourier NARDL extends the Nonlinear ARDL (NARDL) bounds-testing framework by adding Fourier trigonometric terms to the error-correction equation, allowing the model to capture smooth, gradual structural breaks in the long-run relationship w...
Fourier OLS
Fourier OLS is an OLS regression extended by adding low-frequency trigonometric (sine and cosine) terms to the regressor matrix. These Fourier components approximate smooth, gradual structural changes in the regression relationship over tim...
Fourier PP unit root test
The Fourier PP unit root test extends the classical Phillips-Perron test by embedding low-frequency Fourier terms in the deterministic component, enabling the test to account for an unknown number of smooth, gradual structural breaks in the...
Fourier Panel Data Analysis
Fourier panel data analysis embeds trigonometric sine and cosine terms into a standard panel regression to approximate smooth, gradual structural shifts in the data-generating process. Rather than assuming a sharp break at a known date, the...
Fourier Quantile-on-Quantile Regression
Fourier quantile-on-quantile regression extends the quantile-on-quantile (QQ) framework of Sim and Zhou (2015) by embedding Fourier trigonometric terms into the local linear quantile model. This allows the estimated dependence between the q...
Fourier Random Effects Model
The Fourier Random Effects Model extends the standard random effects panel estimator by incorporating trigonometric (Fourier) terms to approximate smooth, gradual structural change in time trends or intercepts. It retains the GLS efficiency...
Fourier SARIMA model
The Fourier SARIMA model extends the classical Seasonal ARIMA framework by incorporating trigonometric (Fourier) terms as deterministic regressors. This allows the model to approximate smooth, complex, or multiple-frequency seasonal pattern...
Fourier SVAR Model
The Fourier SVAR model integrates Fourier series approximations into the structural VAR framework, allowing the model to capture smooth, gradual structural breaks and time-varying dynamics in multivariate time series without requiring a pri...
Fourier TGARCH
The Fourier TGARCH model extends the Threshold GARCH framework by embedding Fourier trigonometric terms in the conditional variance equation to capture smooth, gradual structural breaks in volatility dynamics. It jointly models asymmetric l...
Fourier Toda-Yamamoto Causality
The Fourier Toda-Yamamoto (FTY) causality test extends the classical Toda-Yamamoto procedure by embedding Fourier trigonometric terms in the augmented VAR to capture smooth, gradual structural breaks in the deterministic component. It retai...
Fourier VAR model
The Fourier VAR model extends the standard Vector Autoregression by replacing fixed deterministic terms with Fourier trigonometric components, allowing the intercept (and optionally the trend) to shift gradually and smoothly over time. This...
Fourier VECM
The Fourier VECM augments the classical vector error correction model with low-frequency trigonometric terms — sine and cosine components — to capture smooth, gradual structural change in cointegrating relationships without specifying the n...
Fourier WLS
Fourier WLS is a time-series regression technique that embeds low-frequency Fourier trigonometric terms into a Weighted Least Squares framework to capture smooth, gradual structural breaks in means or trends without requiring the researcher...
Fourier Zivot-Andrews test
The Fourier Zivot-Andrews test extends the classic Zivot-Andrews (1992) unit root test by replacing sharp, single structural break dummies with a low-frequency Fourier approximation, allowing the test to accommodate smooth, gradual, and mul...
Fourier system GMM
Fourier system GMM embeds Fourier trigonometric terms into the System GMM estimator of Blundell and Bond (1998) to accommodate smooth, gradual structural breaks in dynamic panel data. By adding sine and cosine components as regressors, the...
Frailty Model
The shared frailty model, introduced by Vaupel, Manton, and Stallard in 1979, extends standard survival regression by incorporating a random effect — the 'frailty' — that captures unobserved heterogeneity among subjects or clusters. When su...