قارن الطرق

	نموذج ARMA (متوسط متحرك ذاتي الانحدار)	نموذج ARIMA (الانحدار الذاتي المتكامل المتوسط المتحرك)	نموذج الانحدار الذاتي (AR)	نموذج المتوسط المتحرك (MA)	نموذج SARIMA
المجال	الاقتصاد القياسي	الاقتصاد القياسي	الاقتصاد القياسي	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model	Regression model	Regression model	Regression model
سنة النشأة	1970	1970	1970s (popularised 1976)	1970	1970 (first edition); 1976 (revised)
صاحب الطريقة	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Box and Jenkins	Box, Jenkins, and Reinsel
النوع	Time series model	Time series forecasting model	Time series model	Linear time series model	Seasonal time series model
المصدر التأسيسي	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043	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., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744
الأسماء البديلة	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	AR model, AR(p) model, autoregression, AR process	MA model, MA(q) process, moving-average process, Box-Jenkins MA	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
ذات صلة	5	6	6	5	5
الملخص	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.	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.	An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial series.	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.	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.