เปรียบเทียบวิธี

	การทดสอบความเป็นเหตุเป็นผลแบบ Toda-Yamamoto Granger	แบบจำลอง Vector Autoregression (VAR)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Hypothesis test	Regression model
ปีกำเนิด	1995	2005
ผู้ริเริ่ม	Hiro Toda & Taku Yamamoto	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
ประเภท	Modified Wald test on augmented VAR	Multivariate time-series model
แหล่งต้นตำรับ	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
ชื่อเรียกอื่น	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
ที่เกี่ยวข้อง	3	4
สรุป	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.	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).