مقایسهٔ روش‌ها

	مدل میانگین متحرک (MA)	مدل ARMA (میانگین متحرک خودرگرسیو)	مدل SARIMA
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1970	1970	1970 (first edition); 1976 (revised)
پدیدآور	Box and Jenkins	George E. P. Box and Gwilym M. Jenkins	Box, Jenkins, and Reinsel
نوع	Linear time series model	Time series model	Seasonal time series model
منبع بنیادین	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
نام‌های دیگر	MA model, MA(q) process, moving-average process, Box-Jenkins MA	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
مرتبط	5	5	5
خلاصه	The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itself, the MA model uses lagged error terms, making it well-suited for capturing short-lived disturbances that dissipate over q periods.	The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting.	SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse for univariate seasonal time series forecasting in econometrics, economics, and official statistics.