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| 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 |
| Họ | Regression model | Regression model | Regression model |
| Năm ra đời≠ | 1970 | 1970s (popularised 1976) | 1970 |
| Người khởi xướng≠ | George Box and Gwilym Jenkins | George E. P. Box and Gwilym M. Jenkins | Box and Jenkins |
| Loại≠ | 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. link ↗ | 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 | 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≠ | 6 | 6 | 5 |
| Tóm tắt≠ | 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. |
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