قارن الطرق

	نموذج المتوسط المتحرك فورييه (Fourier MA)	نموذج فورييه ARIMA
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	1990s–2000s	2004-2012
صاحب الطريقة	Harvey, A. C.; Hyndman, R. J.	Becker, Enders, and Hurn; further extended by Enders and Lee
النوع	Time series model	Time series model
المصدر التأسيسي	Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-202.
الأسماء البديلة	Fourier MA, Fourier-augmented moving average, trigonometric MA model, harmonic moving average model	Fourier ARIMA, ARIMA with Fourier terms, trigonometric ARIMA, Fourier-flexible ARIMA
ذات صلة	2	2
الملخص	The Fourier MA model combines a Moving Average (MA) error structure with Fourier series terms — sine and cosine pairs — to capture complex or high-frequency seasonal patterns in time series data. It is particularly useful when the seasonal period is long or irregular, making classical seasonal ARIMA parameterisation infeasible.	The Fourier ARIMA model augments a standard ARIMA specification with trigonometric sine and cosine terms, allowing it to capture smooth, gradual structural change and flexible nonlinear seasonality without specifying the exact timing or number of breaks in advance. It is widely used in applied macroeconometrics and finance for series exhibiting slowly evolving dynamics.