เปรียบเทียบวิธี

	แบบจำลองฟูเรียร์ ARCH	แบบจำลอง Fourier GARCH
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model
ปีกำเนิด	2010s	2000–2012
ผู้ริเริ่ม	Extends Engle (1982) ARCH framework with Fourier terms following Enders & Lee (2012)	Ludlow & Enders (2000); extended by Enders & Lee (2012) Fourier framework
ประเภท	Volatility model with smooth structural change	Volatility model
แหล่งต้นตำรับ	Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.	Ludlow, J., & Enders, W. (2000). Estimating non-linear ARMA models using Fourier coefficients. International Journal of Forecasting, 16(3), 333–347.
ชื่อเรียกอื่น	Fourier-ARCH, F-ARCH, ARCH with Fourier terms, Fourier smooth transition ARCH	Fourier GARCH, Fourier-flexible GARCH, GARCH with Fourier terms, smooth-break GARCH
ที่เกี่ยวข้อง	6	5
สรุป	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 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.