So sánh phương pháp

	Kiểm định Nhân quả Granger Toda-Yamamoto	Kiểm định nhân quả Granger Dolado-Lütkepohl	Mô hình Tự hồi quy Vector (VAR)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Hypothesis test	Hypothesis test	Regression model
Năm ra đời	1995	1996	2005
Người khởi xướng	Hiro Toda & Taku Yamamoto	Juan Dolado & Helmut Lütkepohl	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Loại	Modified Wald test on augmented VAR	Modified Wald test for Granger causality in possibly integrated or cointegrated VAR systems	Multivariate time-series model
Công trình gốc	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.	Dolado, J. J., & Lütkepohl, H. (1996). Making Wald tests work for cointegrated VAR systems. Econometric Reviews, 15(4), 369–386.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Tên gọi khác	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	DL Causality Test, Modified Wald Causality Test, Augmented VAR Causality Test, Dolado-Lütkepohl Testi	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Liên quan	3	2	4
Tóm tắt	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.	The Dolado-Lütkepohl (DL) test, introduced by Dolado and Lütkepohl (1996), is a modified Wald procedure for testing Granger causality in vector autoregressive (VAR) systems whose variables may be integrated or cointegrated. By fitting a VAR of slightly higher order than necessary and restricting the Wald statistic to the first p lag blocks, the test recovers the standard chi-squared limiting distribution without requiring pre-testing for cointegration or transformation to error-correction form.	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).