So sánh phương pháp

	GMM Hệ thống Fourier	Kiểm định giới hạn ARDL Fourier
Lĩnh vực	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model
Năm ra đời	2000s–2010s	2001-2021
Người khởi xướng	Blundell & Bond (System GMM, 1998); Fourier augmentation adapted from Gallant (1981) and Becker, Enders & Lee (2006)	Pesaran, Shin & Smith (ARDL foundation); Fourier extension by Nazlioglu and related authors
Loại	Dynamic panel GMM with Fourier smooth-break regressors	Cointegration / bounds test
Công trình gốc	Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115–143.	Nazlioglu, S., Gormus, A., & Soytas, U. (2021). Oil prices and monetary policy in emerging markets: structural breaks, asymmetries, and Fourier approximations. Energy Economics, 95, 105119.
Tên gọi khác	Fourier System GMM, Fourier-augmented Blundell-Bond GMM, smooth-break system GMM, Fourier SGMM	Fourier ARDL, Fourier bounds testing, ARDL with Fourier approximation, F-ARDL cointegration test
Liên quan	6	5
Tóm tắt	Fourier system GMM embeds Fourier trigonometric terms into the System GMM estimator of Blundell and Bond (1998) to accommodate smooth, gradual structural breaks in dynamic panel data. By adding sine and cosine components as regressors, the estimator captures unknown, potentially multiple regime shifts without requiring prior knowledge of break dates, while preserving the instrument-based controls for endogeneity and individual fixed effects.	The Fourier ARDL bounds test augments the Pesaran-Shin-Smith cointegration framework with trigonometric (Fourier) terms that capture gradual, smooth structural breaks in the data-generating process. It tests for a long-run level relationship between variables without requiring the researcher to specify the number, timing, or form of structural breaks in advance.