Σύγκριση μεθόδων

	Αιτιότητα Toda-Yamamoto με Χρονικά Μεταβαλλόμενες Παραμέτρους	Μοντέλο Αυτοπαλινδρόμησης Διανυσμάτων (VAR)
Πεδίο	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model
Έτος προέλευσης	1995 (base); TVP variant emerged early 2000s–2010s	2005
Δημιουργός	Toda & Yamamoto (1995); TVP extension by subsequent applied econometricians	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Τύπος	Causality test (time-varying)	Multivariate time-series model
Θεμελιώδης πηγή	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.
Εναλλακτικές ονομασίες	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
Συναφείς	3	4
Σύνοψη	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).