So sánh phương pháp

	Kiểm định nhân quả Granger Fourier Toda-Yamamoto	Kiểm định Nhân quả Granger Toda-Yamamoto
Lĩnh vực	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Hypothesis test
Năm ra đời	2019	1995
Người khởi xướng	Yilanci, Ozgur (building on Toda and Yamamoto 1995; Becker, Enders, and Hurn 2004)	Hiro Toda & Taku Yamamoto
Loại	Granger causality test	Modified Wald test on augmented VAR
Công trình gốc	Yilanci, V., & Ozgur, O. (2019). Testing the Fourier Toda-Yamamoto causality test with an application to energy demand. Energy Economics, 84, 104498.	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.
Tên gọi khác	FTY causality, Fourier TY causality, Toda-Yamamoto causality with Fourier approximation, FTY Granger causality	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi
Liên quan	3	3
Tóm tắt	The Fourier Toda-Yamamoto (FTY) causality test extends the classical Toda-Yamamoto procedure by embedding Fourier trigonometric terms in the augmented VAR to capture smooth, gradual structural breaks in the deterministic component. It retains the key advantage of the Toda-Yamamoto approach — Granger causality can be tested without pre-testing for integration or cointegration order — while dramatically improving size and power when breaks occur.	The Toda-Yamamoto (TY) causality test, introduced by Toda and Yamamoto (1995), provides a robust procedure for testing Granger non-causality in vector autoregressive (VAR) models when the variables may be integrated or cointegrated of arbitrary order. By intentionally over-fitting the VAR with extra lags equal to the maximum integration order, the method bypasses the need for pre-testing cointegration and preserves the standard asymptotic chi-squared distribution of the Wald statistic.