قارن الطرق

	تحليل بيانات البانل باستخدام متسلسلة فورييه	اختبار سببية غرانجر باستخدام فورير
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	2006 (Fourier framework); panel extensions 2010s	2016
صاحب الطريقة	Becker, Enders, and Lee (Fourier unit root framework); extended to panel data by subsequent applied econometricians	Enders and Jones
النوع	Panel regression with Fourier terms	Causality test
المصدر التأسيسي	Becker, R., Enders, W., & Lee, J. (2006). A stationary 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 panel regression, smooth structural break panel model, trigonometric panel data model, Fourier-flexible panel estimator	Fourier Granger causality test, Enders-Jones Granger causality, smooth structural break Granger test, spectral Granger causality
ذات صلة	6	6
الملخص	Fourier panel data analysis embeds trigonometric sine and cosine terms into a standard panel regression to approximate smooth, gradual structural shifts in the data-generating process. Rather than assuming a sharp break at a known date, the Fourier approach lets the data reveal the timing and shape of any structural change through a flexible trigonometric approximation, while retaining the cross-sectional and time-series structure of panel data.	The Fourier Granger causality test extends the classic Granger causality framework by embedding low-frequency Fourier terms in the VAR equation, allowing the causal relationship to shift gradually over time without requiring the researcher to pre-specify the number or location of structural breaks.