So sánh phương pháp

	Mô hình ARMA (Autoregressive Moving Average)	Mô hình ARIMA (Autoregressive Integrated Moving Average)	Mô hình Tự hồi quy (AR)	Mô hình Trung bình Trượt (MA)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Regression model	Regression model
Năm ra đời	1970	1970	1970s (popularised 1976)	1970
Người khởi xướng	George E. P. Box and Gwilym M. Jenkins	George Box and Gwilym Jenkins	George E. P. Box and Gwilym M. Jenkins	Box and Jenkins
Loại	Time series model	Time series forecasting model	Time series model	Linear time series model
Công trình gốc	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
Tên gọi khác	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
Liên quan	5	6	6	5
Tóm tắt	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.