เปรียบเทียบวิธี

	การทดสอบความเป็นเหตุเป็นผลแบบ Granger ของ Dolado-Lütkepohl	การทดสอบความเป็นเหตุเป็นผลแบบแกรนเจอร์ (Granger Causality Test)	การทดสอบความเป็นเหตุเป็นผลแบบ Toda-Yamamoto Granger
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Hypothesis test	Regression model	Hypothesis test
ปีกำเนิด	1996	1969	1995
ผู้ริเริ่ม	Juan Dolado & Helmut Lütkepohl	Clive W. J. Granger	Hiro Toda & Taku Yamamoto
ประเภท	Modified Wald test for Granger causality in possibly integrated or cointegrated VAR systems	Time-series predictive causality test	Modified Wald test on augmented VAR
แหล่งต้นตำรับ	Dolado, J. J., & Lütkepohl, H. (1996). Making Wald tests work for cointegrated VAR systems. Econometric Reviews, 15(4), 369–386.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.
ชื่อเรียกอื่น	DL Causality Test, Modified Wald Causality Test, Augmented VAR Causality Test, Dolado-Lütkepohl Testi	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi
ที่เกี่ยวข้อง	2	5	3
สรุป	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.	The Granger causality test, introduced by Clive W. J. Granger in 1969, assesses whether the past values of one time series help predict another beyond what the latter's own past already explains. It defines causality in a strictly predictive sense rather than as a structural or physical cause.	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.