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| Modello GARCH di Fourier× | Modello TGARCH (Threshold GARCH)× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 2000–2012 | 1993-1994 |
| Ideatore≠ | Ludlow & Enders (2000); extended by Enders & Lee (2012) Fourier framework | Zakoian (1994); Glosten, Jagannathan & Runkle (1993) |
| Tipo≠ | Volatility model | Asymmetric volatility model |
| Fonte seminale≠ | Ludlow, J., & Enders, W. (2000). Estimating non-linear ARMA models using Fourier coefficients. International Journal of Forecasting, 16(3), 333–347. DOI ↗ | Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931-955. DOI ↗ |
| Alias | Fourier GARCH, Fourier-flexible GARCH, GARCH with Fourier terms, smooth-break GARCH | Threshold GARCH, TGARCH, GJR-GARCH, asymmetric GARCH |
| Correlati≠ | 5 | 6 |
| Sintesi≠ | 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 Threshold GARCH (TGARCH) model extends the standard GARCH framework by allowing positive and negative return shocks to have asymmetric effects on conditional variance. Negative shocks — bad news — typically amplify volatility more than positive shocks of the same magnitude, a stylised fact known as the leverage effect. TGARCH captures this asymmetry through a threshold indicator that switches on when the previous period's shock was negative. |
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