مقایسهٔ روش‌ها

	آزمون هم‌انباشتگی یوهانسن فوریه	آزمون هم‌انباشتگی انگل-گرنجر
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2012 (Fourier extension); 1988 (Johansen original)	1987
پدیدآور	Enders & Lee (Fourier extension); Johansen (original trace/max-eigenvalue test)	Robert F. Engle and Clive W. J. Granger
نوع	Cointegration test with smooth structural breaks	Cointegration test
منبع بنیادین	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.	Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276.
نام‌های دیگر	Fourier Johansen test, Fourier-Johansen trace test, smooth-break Johansen cointegration, FJ cointegration	EG cointegration test, Engle-Granger two-step method, residual-based cointegration test, EG test
مرتبط	5	5
خلاصه	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 Engle-Granger two-step method tests whether two or more non-stationary I(1) time series share a common stochastic trend — that is, whether a linear combination of them is stationary. If cointegration is confirmed, an error-correction model (ECM) can be estimated to capture both short-run dynamics and long-run equilibrium adjustment.