Linganisha mbinu

	Kipimo cha Utafiti wa Kiasababishi cha Toda-Yamamoto	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1995	1970
Mwanzilishi	Toda, H. Y. and Yamamoto, T.	George Box and Gwilym Jenkins
Aina	Causality test	Time series forecasting 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.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Majina mbadala	Toda-Yamamoto test, TY causality test, modified Wald test for Granger causality, TY-MWALD	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
Zinazohusiana	5	6
Muhtasari	The Toda-Yamamoto (TY) causality test is a modified Wald procedure for testing Granger causality in vector autoregressions (VARs) estimated in levels, even when variables are nonstationary or cointegrated. By intentionally over-fitting the VAR with extra lags equal to the maximum integration order, it restores the standard chi-squared asymptotic distribution of the Wald statistic without requiring prior unit-root or cointegration pretesting.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.