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| Model Fouriera ARCH× | Model ARCH z przerwami strukturalnymi× | |
|---|---|---|
| Dziedzina | Ekonometria | Ekonometria |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 2010s | 1982–1990 |
| Twórca≠ | Extends Engle (1982) ARCH framework with Fourier terms following Enders & Lee (2012) | Engle (1982) for ARCH; Lamoureux & Lastrapes (1990) for break-adjusted variance persistence |
| Typ≠ | Volatility model with smooth structural change | Volatility model with regime change |
| 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 | ARCH with structural breaks, break-adjusted ARCH, regime-switching ARCH, SB-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 Structural Break ARCH model extends Engle's (1982) Autoregressive Conditional Heteroscedasticity framework by explicitly accounting for abrupt, permanent shifts in the conditional variance process. Ignoring structural breaks in variance causes ARCH parameters to appear spuriously persistent, so incorporating break dummies or regime-specific parameters yields more accurate volatility estimates and better model fit. |
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