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| Modello ARMA (Autoregressive Moving Average)× | Modello Autoregressivo (AR)× | Modello a Media Mobile (MA)× | |
|---|---|---|---|
| Campo | Econometria | Econometria | Econometria |
| Famiglia | Regression model | Regression model | Regression model |
| Anno di origine≠ | 1970 | 1970s (popularised 1976) | 1970 |
| Ideatore≠ | George E. P. Box and Gwilym M. Jenkins | George E. P. Box and Gwilym M. Jenkins | Box and Jenkins |
| Tipo≠ | Time series model | Time series model | Linear time series model |
| Fonte seminale≠ | 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 |
| Alias | ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q) | AR model, AR(p) model, autoregression, AR process | MA model, MA(q) process, moving-average process, Box-Jenkins MA |
| Correlati≠ | 5 | 6 | 5 |
| Sintesi≠ | 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. | 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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