Σύγκριση μεθόδων

	Δοκιμή Αιτιότητας Granger	Έλεγχος Συνολοκλήρωσης (Johansen / Engle-Granger)	Παλινδρόμηση Ελαχίστων Τετραγώνων (OLS)	Μοντέλο Αυτοπαλινδρόμησης Διανυσμάτων (VAR)
Πεδίο	Οικονομετρία	Οικονομετρία	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model	Regression model	Regression model
Έτος προέλευσης	1969	1988	2019	2005
Δημιουργός	Clive W. J. Granger	Engle & Granger (1987); Johansen (1988)	Wooldridge (textbook treatment); classical least squares	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
Τύπος	Time-series predictive causality test	Time-series cointegration test	Linear regression	Multivariate time-series model
Θεμελιώδης πηγή	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.	Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
Εναλλακτικές ονομασίες	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi	Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
Συναφείς	5	5	5	4
Σύνοψη	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 cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988).	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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).