مقایسهٔ روش‌ها

	مدل خودبازگشتی فوریه (Fourier AR Model)	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2012	1970
پدیدآور	Enders & Lee	George Box and Gwilym Jenkins
نوع	Time series model with Fourier augmentation	Time series forecasting model
منبع بنیادین	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.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
نام‌های دیگر	Fourier AR, trigonometric AR model, smooth transition AR with Fourier terms, FAR model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
مرتبط	6	6
خلاصه	The Fourier AR model extends the standard autoregressive specification by adding trigonometric (sine and cosine) terms to the deterministic component. This allows the model to capture smooth, gradual shifts in the mean or trend of a time series without requiring the researcher to locate or count structural break points explicitly.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.