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| ARMA-model (Autoregressiv glidende gennemsnit)× | Autoregressiv model (AR)× | SARIMA-model× | |
|---|---|---|---|
| Fagområde | Økonometri | Økonometri | Økonometri |
| Familie | Regression model | Regression model | Regression model |
| Oprindelsesår≠ | 1970 | 1970s (popularised 1976) | 1970 (first edition); 1976 (revised) |
| Ophavsperson≠ | George E. P. Box and Gwilym M. Jenkins | George E. P. Box and Gwilym M. Jenkins | Box, Jenkins, and Reinsel |
| Type≠ | Time series model | Time series model | Seasonal time series model |
| Oprindelig kilde≠ | 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 |
| Aliasser | ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q) | AR model, AR(p) model, autoregression, AR process | SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component |
| Relaterede≠ | 5 | 6 | 5 |
| Resumé≠ | 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. | 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. |
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