مقایسهٔ روش‌ها

	آزمون علیت گرنجر Toda-Yamamoto فوریه	مدل خودرگرسیون برداری (VAR)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2019	2005
پدیدآور	Yilanci, Ozgur (building on Toda and Yamamoto 1995; Becker, Enders, and Hurn 2004)	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
نوع	Granger causality test	Multivariate time-series model
منبع بنیادین	Yilanci, V., & Ozgur, O. (2019). Testing the Fourier Toda-Yamamoto causality test with an application to energy demand. Energy Economics, 84, 104498.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
نام‌های دیگر	FTY causality, Fourier TY causality, Toda-Yamamoto causality with Fourier approximation, FTY Granger causality	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
مرتبط	3	4
خلاصه	The Fourier Toda-Yamamoto (FTY) causality test extends the classical Toda-Yamamoto procedure by embedding Fourier trigonometric terms in the augmented VAR to capture smooth, gradual structural breaks in the deterministic component. It retains the key advantage of the Toda-Yamamoto approach — Granger causality can be tested without pre-testing for integration or cointegration order — while dramatically improving size and power when breaks occur.	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).