Linganisha mbinu

	Uchunguzi wa Uasaba wa Toda-Yamamoto wenye Vigezo Vinavyobadilika kwa Wakati	Muundo wa Uhusiano wa Kiotomatiki wa Vecta (VAR)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1995 (base); TVP variant emerged early 2000s–2010s	2005
Mwanzilishi	Toda & Yamamoto (1995); TVP extension by subsequent applied econometricians	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Aina	Causality test (time-varying)	Multivariate time-series model
Chanzo asilia	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.
Majina mbadala	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
Zinazohusiana	3	4
Muhtasari	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).