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| ARMA model (Autoregresivni pokretni prosek)× | ARIMA model (Autoregresivni integrisani model pokretnih proseka)× | Autoregresivni model (AR)× | SARIMA model× | |
|---|---|---|---|---|
| Oblast | Ekonometrija | Ekonometrija | Ekonometrija | Ekonometrija |
| Porodica | Regression model | Regression model | Regression model | Regression model |
| Godina nastanka≠ | 1970 | 1970 | 1970s (popularised 1976) | 1970 (first edition); 1976 (revised) |
| Tvorac≠ | George E. P. Box and Gwilym M. Jenkins | George Box and Gwilym Jenkins | George E. P. Box and Gwilym M. Jenkins | Box, Jenkins, and Reinsel |
| Tip≠ | Time series model | Time series forecasting model | Time series model | Seasonal time series model |
| Temeljni izvor≠ | Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day. link ↗ | 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 |
| Drugi nazivi | 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 | SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component |
| Srodne≠ | 5 | 6 | 6 | 5 |
| Sažetak≠ | 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. | 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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