Linganisha mbinu

	Mfumo wa Fourier TGARCH	Fourier EGARCH: Uundaji wa Volatiliti kwa Mapumziko Laini ya Kimuundo
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1994 / 2012	2010s
Mwanzilishi	Zakoian (1994) for TGARCH; Enders and Lee (2012) for Fourier approximation framework	Extension of Nelson (1991) EGARCH using Fourier approximation frameworks
Aina	Volatility model with asymmetric leverage and Fourier smooth breaks	Volatility model with smooth structural breaks
Chanzo asilia	Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931-955.	Enders, W., & Lee, J. (2012). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574-599.
Majina mbadala	Fourier TGARCH, Fourier Threshold GARCH, Fourier GJR-GARCH, smooth structural break TGARCH	Fourier-EGARCH, F-EGARCH, Fourier exponential GARCH, smooth structural break EGARCH
Zinazohusiana	5	3
Muhtasari	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.	Fourier EGARCH extends Nelson's (1991) Exponential GARCH model by embedding Fourier trigonometric terms in the conditional variance equation to capture smooth, gradual shifts in the unconditional variance level over time. This allows the model to handle structural breaks in volatility without requiring prior knowledge of their timing or number.