Linganisha mbinu

	Kipimo cha Uhalisia wa Kimahesabu cha Toda-Yamamoto kisicho na Mstari	Kipimo cha Umuhimu cha Granger cha Toda-Yamamoto
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Hypothesis test
Mwaka wa asili	1995 (base); nonlinear extensions 2000s–2010s	1995
Mwanzilishi	Toda & Yamamoto (1995) for the linear base; nonlinear extension developed by subsequent researchers applying rank transformations or neural-network-augmented VAR	Hiro Toda & Taku Yamamoto
Aina	Causality test	Modified Wald test on augmented VAR
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.	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1–2), 225–250.
Majina mbadala	nonlinear TY causality, rank-based Toda-Yamamoto test, modified Wald nonlinear causality, NTY causality test	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi
Zinazohusiana	5	3
Muhtasari	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 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.