Linganisha mbinu

	Fourier EGARCH: Uundaji wa Volatiliti kwa Mapumziko Laini ya Kimuundo	Exponential GARCH (EGARCH)	GJR-GARCH (GARCH Asymmetric)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2010s	1991	1993
Mwanzilishi	Extension of Nelson (1991) EGARCH using Fourier approximation frameworks	Nelson	Glosten, Jagannathan & Runkle (1993); Zakoian (1994)
Aina	Volatility model with smooth structural breaks	Conditional volatility model (asymmetric GARCH variant)	Asymmetric conditional volatility model
Chanzo asilia	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.	Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370.	Glosten, L. R., Jagannathan, R. & Runkle, D. E. (1993). On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48(5), 1779-1801.
Majina mbadala	Fourier-EGARCH, F-EGARCH, Fourier exponential GARCH, smooth structural break EGARCH	exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH	asymmetric GARCH, leverage GARCH, TGARCH, GJR-GARCH — Asimetrik GARCH (Glosten-Jagannathan-Runkle)
Zinazohusiana	3	4	5
Muhtasari	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.	EGARCH is an asymmetric GARCH variant, introduced by Nelson in 1991, that models the leverage effect in which bad news raises volatility more than good news of the same size. It captures the negative-shock asymmetry of financial return series by modelling the logarithm of the conditional variance.	GJR-GARCH is a variant of the GARCH conditional-volatility model that captures the asymmetric effect of negative shocks on volatility using an indicator variable. It was introduced by Glosten, Jagannathan and Runkle (1993), with a closely related threshold formulation by Zakoian (1994).