مقایسهٔ روش‌ها

	آزمون هم‌انباشتگی یوهانسن فوریه	آزمون ریشه واحد فورייה ADF
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2012 (Fourier extension); 1988 (Johansen original)	2006-2012
پدیدآور	Enders & Lee (Fourier extension); Johansen (original trace/max-eigenvalue test)	Becker, Enders, and Lee; Enders and Lee
نوع	Cointegration test with smooth structural breaks	Unit root test with smooth structural breaks
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.	Becker, R., Enders, W., & Lee, J. (2006). A stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis, 27(3), 381-409.
نام‌های دیگر	Fourier Johansen test, Fourier-Johansen trace test, smooth-break Johansen cointegration, FJ cointegration	Fourier ADF test, FADF test, Flexible Fourier ADF, Fourier-based ADF unit root test
مرتبط	5	6
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 Fourier ADF unit root test extends the standard Augmented Dickey-Fuller framework by incorporating low-frequency Fourier terms into the deterministic component. This allows the test to approximate smooth, gradual structural breaks in the level or trend of a time series without requiring prior knowledge of break number, timing, or form.