方法对比

	移动平均（MA）模型	自回归积分滑动平均模型 (ARIMA)	自回归模型 (AR)	SARIMA模型
领域	计量经济学	计量经济学	计量经济学	计量经济学
方法族	Regression model	Regression model	Regression model	Regression model
起源年份	1970	1970	1970s (popularised 1976)	1970 (first edition); 1976 (revised)
提出者	Box and Jenkins	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Box, Jenkins, and Reinsel
类型	Linear time series model	Time series forecasting model	Time series model	Seasonal time series model
开创性文献	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. (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
别名	MA model, MA(q) process, moving-average process, Box-Jenkins MA	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	AR model, AR(p) model, autoregression, AR process	SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component
相关	5	6	6	5
摘要	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 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.	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.