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| Fourier-GARCH-Modell× | EGARCH-Modell (Exponential GARCH)× | |
|---|---|---|
| Fachgebiet | Ökonometrie | Ökonometrie |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 2000–2012 | 1991 |
| Urheber≠ | Ludlow & Enders (2000); extended by Enders & Lee (2012) Fourier framework | Daniel B. Nelson |
| Typ≠ | Volatility model | Volatility / conditional variance model |
| Wegweisende Quelle≠ | Ludlow, J., & Enders, W. (2000). Estimating non-linear ARMA models using Fourier coefficients. International Journal of Forecasting, 16(3), 333–347. DOI ↗ | Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370. DOI ↗ |
| Aliasnamen | Fourier GARCH, Fourier-flexible GARCH, GARCH with Fourier terms, smooth-break GARCH | Exponential GARCH, EGARCH, Nelson EGARCH, log-GARCH |
| Verwandt≠ | 5 | 6 |
| Zusammenfassung≠ | 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 unknown break patterns with sinusoidal functions, it jointly models volatility clustering and time-varying unconditional variance. | 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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