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| SARIMAX× | ARIMA (Autoregressive Integrated Moving Average) Modell× | Tillståndsrumsmodell (Kalmanfilter)× | |
|---|---|---|---|
| Ämnesområde | Ekonometri | Ekonometri | Ekonometri |
| Familj | Regression model | Regression model | Regression model |
| Ursprungsår≠ | 2015 | 2015 | 1990 |
| Upphovsperson≠ | Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors | Box & Jenkins (Box-Jenkins methodology) | Harvey; Durbin & Koopman (state space treatment); Kalman filter |
| Typ≠ | Seasonal time-series regression model | Univariate time-series model | State space time series model |
| Ursprungskälla≠ | Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts. link ↗ | Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021 | Harvey, A. C. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press. DOI ↗ |
| Alias≠ | seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA | Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli | state space, Kalman filter, unobserved components model, Durum Uzayı Modeli (State Space / Kalman Filter) |
| Närliggande≠ | 4 | 5 | 4 |
| Sammanfattning≠ | SARIMAX extends the seasonal ARIMA (Box-Jenkins) model by adding exogenous explanatory variables, so it can capture the effect of holidays, economic indicators, or policy variables on a time series. It combines non-seasonal and seasonal autoregressive and moving-average dynamics with external regressors, and is estimated by maximum likelihood in state-space form. | ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015). | A state space model is a general time series framework that describes a series through unobserved (latent) state variables linked by a measurement equation and a transition equation, with the states estimated in real time by the Kalman filter. Developed in the state space tradition of Harvey (1990) and Durbin & Koopman (2012), it nests ARIMA and exponential smoothing as special cases. |
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