เปรียบเทียบวิธี

	การทดสอบความเป็นเหตุเป็นผลแบบ Toda-Yamamoto ที่มีพารามิเตอร์แปรผันตามเวลา	แบบจำลอง Vector Autoregression (VAR)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model
ปีกำเนิด	1995 (base); TVP variant emerged early 2000s–2010s	2005
ผู้ริเริ่ม	Toda & Yamamoto (1995); TVP extension by subsequent applied econometricians	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
ประเภท	Causality test (time-varying)	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	TVP-TY causality, time-varying Toda-Yamamoto, TVP Granger causality (Toda-Yamamoto), rolling/recursive Toda-Yamamoto causality	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
ที่เกี่ยวข้อง	3	4
สรุป	The TVP Toda-Yamamoto causality test combines Toda and Yamamoto's (1995) augmented VAR approach — which handles possibly integrated or cointegrated series without pre-testing for unit roots — with time-varying parameters, allowing causal relationships between variables to shift across different periods rather than remaining fixed throughout the sample.	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).