Сравнение на методи

	Тест за причинност на Фурие-Тода-Ямамото по Грейнджър	Тест за причинност на Грейнджър	Тест за причинност на Toda-Yamamoto Granger	Модел на векторна авторегресия (VAR)
Област	Иконометрия	Иконометрия	Иконометрия	Иконометрия
Семейство	Regression model	Regression model	Hypothesis test	Regression model
Година на възникване	2019	1969	1995	2005
Създател	Yilanci, Ozgur (building on Toda and Yamamoto 1995; Becker, Enders, and Hurn 2004)	Clive W. J. Granger	Hiro Toda & Taku Yamamoto	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Тип	Granger causality test	Time-series predictive causality test	Modified Wald test on augmented VAR	Multivariate time-series model
Основополагащ източник	Yilanci, V., & Ozgur, O. (2019). Testing the Fourier Toda-Yamamoto causality test with an application to energy demand. Energy Economics, 84, 104498.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.	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.
Други названия	FTY causality, Fourier TY causality, Toda-Yamamoto causality with Fourier approximation, FTY Granger causality	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi	TY Causality Test, Modified Wald Granger Causality, MWALD Test, Toda-Yamamoto Nedensellik Testi	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Свързани	3	5	3	4
Резюме	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.	The Granger causality test, introduced by Clive W. J. Granger in 1969, assesses whether the past values of one time series help predict another beyond what the latter's own past already explains. It defines causality in a strictly predictive sense rather than as a structural or physical cause.	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.	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).