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| Model TGARCH z szeregami Fouriera× | Model EGARCH (Exponential GARCH)× | |
|---|---|---|
| Dziedzina | Ekonometria | Ekonometria |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1994 / 2012 | 1991 |
| Twórca≠ | Zakoian (1994) for TGARCH; Enders and Lee (2012) for Fourier approximation framework | Daniel B. Nelson |
| Typ≠ | Volatility model with asymmetric leverage and Fourier smooth breaks | Volatility / conditional variance model |
| Źródło pierwotne≠ | Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931-955. DOI ↗ | Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370. DOI ↗ |
| Inne nazwy | Fourier TGARCH, Fourier Threshold GARCH, Fourier GJR-GARCH, smooth structural break TGARCH | Exponential GARCH, EGARCH, Nelson EGARCH, log-GARCH |
| Pokrewne≠ | 5 | 6 |
| Podsumowanie≠ | 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 leverage effects — where negative shocks amplify volatility more than positive shocks of the same magnitude — and time-varying intercept shifts caused by unobserved structural change. | The Exponential GARCH (EGARCH) model, introduced by Nelson (1991), extends the standard GARCH framework by modelling the logarithm of conditional variance. This ensures variance is always positive without parameter constraints and, crucially, allows negative and positive shocks to have asymmetric effects on volatility — capturing the well-known leverage effect in financial markets. |
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