Linganisha mbinu

	Mtihani wa Uhalali wa Granger wa Fourier Toda-Yamamoto	Kipimo cha Granger Causality	Muundo wa Uhusiano wa Kiotomatiki wa Vecta (VAR)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2019	1969	2005
Mwanzilishi	Yilanci, Ozgur (building on Toda and Yamamoto 1995; Becker, Enders, and Hurn 2004)	Clive W. J. Granger	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Aina	Granger causality test	Time-series predictive causality test	Multivariate time-series model
Chanzo asilia	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.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Majina mbadala	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	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Zinazohusiana	3	5	4
Muhtasari	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.	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).