Σύγκριση μεθόδων

	Μη Γραμμικός Έλεγχος Αιτιότητας Toda-Yamamoto	Έλεγχος Συνολοκλήρωσης (Johansen / Engle-Granger)
Πεδίο	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model
Έτος προέλευσης	1995 (base); nonlinear extensions 2000s–2010s	1988
Δημιουργός	Toda & Yamamoto (1995) for the linear base; nonlinear extension developed by subsequent researchers applying rank transformations or neural-network-augmented VAR	Engle & Granger (1987); Johansen (1988)
Τύπος	Causality test	Time-series cointegration test
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.	Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254.
Εναλλακτικές ονομασίες	nonlinear TY causality, rank-based Toda-Yamamoto test, modified Wald nonlinear causality, NTY causality test	Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)
Συναφείς	5	5
Σύνοψη	The Nonlinear Toda-Yamamoto causality test extends the classic Toda-Yamamoto (1995) modified Wald procedure to detect causal linkages that are hidden in the means of series but manifest through nonlinear dynamics such as asymmetries, threshold effects, or volatility transmission. It fits an augmented VAR on rank-transformed or otherwise nonlinearly mapped series and applies a chi-squared Wald test on the extra-lag coefficients.	The cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988).