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| Model Fouriera ARCH× | Model ARCH z parametrami zmiennymi w czasie (TVP-ARCH)× | |
|---|---|---|
| Dziedzina | Ekonometria | Ekonometria |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 2010s | 1980s–1990s |
| Twórca≠ | Extends Engle (1982) ARCH framework with Fourier terms following Enders & Lee (2012) | Extension of Engle (1982) ARCH; TVP-ARCH formalization credited to Nicholls & Quinn and subsequent state-space literature |
| Typ≠ | Volatility model with smooth structural change | Conditional heteroscedasticity model with time-varying coefficients |
| Źródło pierwotne | Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. DOI ↗ | Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. DOI ↗ |
| Inne nazwy | Fourier-ARCH, F-ARCH, ARCH with Fourier terms, Fourier smooth transition ARCH | TVP-ARCH, time-varying ARCH, adaptive ARCH, state-space ARCH |
| Pokrewne≠ | 6 | 5 |
| Podsumowanie≠ | The Fourier ARCH model extends the classical ARCH framework by incorporating trigonometric (Fourier) terms into the conditional variance equation. This allows the model to capture smooth, gradual shifts in volatility dynamics over time without assuming abrupt structural breaks, making it well-suited for long financial or macroeconomic time series subject to slowly evolving regime changes. | 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. This makes it possible to capture structural shifts in volatility dynamics without imposing a fixed parameter regime. |
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