قارن الطرق

	نموذج فورييه ARMA	نموذج الانحدار الذاتي المتجه بمتغيرات فورييه (Fourier VAR Model)
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	2004–2006	2010s
صاحب الطريقة	Becker, Enders, and Hurn	Enders & Lee; extended by Nazlioglu and others to VAR systems
النوع	Time series model with smooth structural change	Multivariate time-series model
المصدر التأسيسي	Becker, R., Enders, W., & Hurn, S. (2006). A general test for time dependence in parameters. Journal of Applied Econometrics, 21(7), 1005–1028.	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.
الأسماء البديلة	Fourier ARMA, ARMA with Fourier terms, trigonometric ARMA, smooth structural change ARMA	Fourier VAR, smooth structural break VAR, trigonometric VAR, Fourier-augmented VAR
ذات صلة	5	6
الملخص	The Fourier ARMA model augments the classical Autoregressive Moving Average framework with low-frequency Fourier (sine and cosine) terms to capture smooth, gradual shifts in the mean or trend of a time series. Unlike dummy-variable approaches, it requires no prior knowledge of when structural change occurred, approximating change with flexible trigonometric functions.	The Fourier VAR model extends the standard Vector Autoregression by replacing fixed deterministic terms with Fourier trigonometric components, allowing the intercept (and optionally the trend) to shift gradually and smoothly over time. This eliminates the need to pre-specify the number, timing, or shape of structural breaks in a multivariate time-series system.