قارن الطرق

	اختبار جذر الوحدة ADF فورييه	اختبار التكامل المشترك لفورييه-إنجل-جرانجر
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	2006-2012	2016
صاحب الطريقة	Becker, Enders, and Lee; Enders and Lee	Enders & Jones (2016), extending Engle & Granger (1987)
النوع	Unit root test with smooth structural breaks	Cointegration test
المصدر التأسيسي	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.	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.
الأسماء البديلة	Fourier ADF test, FADF test, Flexible Fourier ADF, Fourier-based ADF unit root test	Fourier EG cointegration, Enders-Jones cointegration test, smooth structural break cointegration, FEGC test
ذات صلة	6	5
الملخص	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.	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.