เปรียบเทียบวิธี

	การทดสอบความเป็นเหตุเป็นผลแบบ Toda-Yamamoto	แบบจำลอง ARIMA (Autoregressive Integrated Moving Average)
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model
ปีกำเนิด	1995	1970
ผู้ริเริ่ม	Toda, H. Y. and Yamamoto, T.	George Box and Gwilym Jenkins
ประเภท	Causality test	Time series forecasting model
แหล่งต้นตำรับ	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.
ชื่อเรียกอื่น	Toda-Yamamoto test, TY causality test, modified Wald test for Granger causality, TY-MWALD	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
ที่เกี่ยวข้อง	5	6
สรุป	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.