Σύγκριση μεθόδων

	Έλεγχος Συνολοκλήρωσης Fourier Johansen	Έλεγχος Συνολοκλήρωσης Johansen με Διαρθρωτική Μεταβολή
Πεδίο	Οικονομετρία	Οικονομετρία
Οικογένεια	Regression model	Regression model
Έτος προέλευσης	2012 (Fourier extension); 1988 (Johansen original)	2000–2001
Δημιουργός	Enders & Lee (Fourier extension); Johansen (original trace/max-eigenvalue test)	Johansen (1988); structural-break extensions by Saikkonen & Lütkepohl (2000) and Lütkepohl, Müller & Saikkonen (2001)
Τύπος	Cointegration test with smooth structural breaks	Cointegration test / VECM estimation
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.	Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2–3), 231–254.
Εναλλακτικές ονομασίες	Fourier Johansen test, Fourier-Johansen trace test, smooth-break Johansen cointegration, FJ cointegration	Johansen cointegration with breaks, break-robust Johansen test, cointegration test with regime shifts, structural change Johansen VECM
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 structural break Johansen cointegration test extends the standard maximum-likelihood Johansen procedure to settings where the multivariate time series exhibits level shifts or trend breaks. By incorporating dummy variables or shift regressors into the VECM, the test determines the cointegrating rank without confounding genuine long-run relationships with regime changes.