Linganisha mbinu

	Muundo wa ARCH wa Fourier (Fourier ARCH Model)	Mfumo wa ARCH wa Mabadiliko ya Kimuundo
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	2010s	1982–1990
Mwanzilishi	Extends Engle (1982) ARCH framework with Fourier terms following Enders & Lee (2012)	Engle (1982) for ARCH; Lamoureux & Lastrapes (1990) for break-adjusted variance persistence
Aina	Volatility model with smooth structural change	Volatility model with regime change
Chanzo asilia	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.
Majina mbadala	Fourier-ARCH, F-ARCH, ARCH with Fourier terms, Fourier smooth transition ARCH	ARCH with structural breaks, break-adjusted ARCH, regime-switching ARCH, SB-ARCH
Zinazohusiana	6	5
Muhtasari	The Fourier ARCH model extends the classical ARCH framework by incorporating trigonometric (Fourier) terms into the conditional variance equation. This allows the model to capture smooth, gradual shifts in volatility dynamics over time without assuming abrupt structural breaks, making it well-suited for long financial or macroeconomic time series subject to slowly evolving regime changes.	The Structural Break ARCH model extends Engle's (1982) Autoregressive Conditional Heteroscedasticity framework by explicitly accounting for abrupt, permanent shifts in the conditional variance process. Ignoring structural breaks in variance causes ARCH parameters to appear spuriously persistent, so incorporating break dummies or regime-specific parameters yields more accurate volatility estimates and better model fit.