Linganisha mbinu

	Muundo wa ARCH wa Fourier (Fourier ARCH Model)	Mfumo wa ARCH wenye Vigezo Vinavyobadilika kwa Wakati (TVP-ARCH)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	2010s	1980s–1990s
Mwanzilishi	Extends Engle (1982) ARCH framework with Fourier terms following Enders & Lee (2012)	Extension of Engle (1982) ARCH; TVP-ARCH formalization credited to Nicholls & Quinn and subsequent state-space literature
Aina	Volatility model with smooth structural change	Conditional heteroscedasticity model with time-varying coefficients
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	TVP-ARCH, time-varying ARCH, adaptive ARCH, state-space 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 Time-Varying Parameter ARCH (TVP-ARCH) model extends the classic ARCH framework by allowing both the conditional mean coefficients and the ARCH variance parameters to drift over time according to a random-walk or state-space process. This makes it possible to capture structural shifts in volatility dynamics without imposing a fixed parameter regime.