Linganisha mbinu

	Kipimo cha Uhalisia wa Kimahesabu cha Toda-Yamamoto kisicho na Mstari	Muundo wa Uhusiano wa Kiotomatiki wa Vecta (VAR)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1995 (base); nonlinear extensions 2000s–2010s	2005
Mwanzilishi	Toda & Yamamoto (1995) for the linear base; nonlinear extension developed by subsequent researchers applying rank transformations or neural-network-augmented VAR	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Aina	Causality test	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	nonlinear TY causality, rank-based Toda-Yamamoto test, modified Wald nonlinear causality, NTY causality test	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Zinazohusiana	5	4
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.	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).