قارن الطرق

	نموذج فورير غير الخطي لنموذج الانحدار الذاتي الموزون (Fourier NARDL)	اختبار التكامل المشترك لفورييه-إنجل-جرانجر
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	2014–2020s	2016
صاحب الطريقة	Extension of Shin, Yu & Greenwood-Nimmo (2014) NARDL, incorporating Fourier terms from Becker, Enders & Lee (2006)	Enders & Jones (2016), extending Engle & Granger (1987)
النوع	Nonlinear cointegrating model with smooth break approximation	Cointegration test
المصدر التأسيسي	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt (pp. 281–314). Springer.	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 NARDL, Fourier nonlinear ARDL, F-NARDL, Fourier asymmetric ARDL	Fourier EG cointegration, Enders-Jones cointegration test, smooth structural break cointegration, FEGC test
ذات صلة	6	5
الملخص	Fourier NARDL extends the Nonlinear ARDL (NARDL) bounds-testing framework by adding Fourier trigonometric terms to the error-correction equation, allowing the model to capture smooth, gradual structural breaks in the long-run relationship without requiring the researcher to know or specify the break date in advance.	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.