Σύγκριση μεθόδων

	Έλεγχος Συνολοκλήρωσης Fourier Johansen	Δοκιμή Συνολοκλήρωσης Fourier Engle-Granger
Πεδίο	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model
Έτος προέλευσης	2012 (Fourier extension); 1988 (Johansen original)	2016
Δημιουργός	Enders & Lee (Fourier extension); Johansen (original trace/max-eigenvalue test)	Enders & Jones (2016), extending Engle & Granger (1987)
Τύπος	Cointegration test with smooth structural breaks	Cointegration test
Θεμελιώδης πηγή	Enders, W., & Lee, J. (2012). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574–599.	Enders, W., & Jones, P. (2016). Grain prices, oil prices, and multiple smooth breaks in a VAR. Studies in Nonlinear Dynamics and Econometrics, 20(4), 399–419.
Εναλλακτικές ονομασίες	Fourier Johansen test, Fourier-Johansen trace test, smooth-break Johansen cointegration, FJ cointegration	Fourier EG cointegration, Enders-Jones cointegration test, smooth structural break cointegration, FEGC test
Συναφείς	5	5
Σύνοψη	The Fourier Johansen cointegration test extends the classical Johansen trace and maximum-eigenvalue tests by embedding low-frequency Fourier terms in the deterministic component of the VECM. This allows the test to remain valid when cointegrating relationships experience gradual, smooth regime shifts that standard Johansen critical values do not accommodate.	The Fourier Engle-Granger cointegration test extends the classic two-step Engle-Granger procedure by embedding low-frequency trigonometric (Fourier) terms in the cointegrating regression. This accommodates an unknown number of smooth structural breaks in the deterministic components without specifying their dates, producing a more powerful test when long-run relationships shift gradually over time.