So sánh phương pháp

	Kiểm định đồng tích hợp Johansen Fourier	Kiểm định đồng liên kết Johansen có điểm đứt gãy cấu trúc
Lĩnh vực	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model
Năm ra đời	2012 (Fourier extension); 1988 (Johansen original)	2000–2001
Người khởi xướng	Enders & Lee (Fourier extension); Johansen (original trace/max-eigenvalue test)	Johansen (1988); structural-break extensions by Saikkonen & Lütkepohl (2000) and Lütkepohl, Müller & Saikkonen (2001)
Loại	Cointegration test with smooth structural breaks	Cointegration test / VECM estimation
Công trình gốc	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.
Tên gọi khác	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
Liên quan	5	5
Tóm tắt	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.