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| ARIMA-Modell (Autoregressives integriertes gleitendes Durchschnittsmodell)× | Autoregressives Modell (AR)× | Robuste verallgemeinerte Kleinste Quadrate (Robuste GLS)× | |
|---|---|---|---|
| Fachgebiet | Ökonometrie | Ökonometrie | Ökonometrie |
| Familie | Regression model | Regression model | Regression model |
| Entstehungsjahr≠ | 1970 | 1970s (popularised 1976) | 1936 / 1980 |
| Urheber≠ | George Box and Gwilym Jenkins | George E. P. Box and Gwilym M. Jenkins | Aitken (GLS theory, 1936); White (robust covariance, 1980) |
| Typ≠ | Time series forecasting model | Time series model | Robust linear regression |
| Wegweisende Quelle≠ | 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 | Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson. Chapter 9: The Generalized Regression Model and Heteroscedasticity. ISBN: 978-0131395381 |
| Aliasnamen | ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q) | AR model, AR(p) model, autoregression, AR process | robust generalized least squares, GLS with robust standard errors, heteroscedasticity-consistent GLS, HC-GLS |
| Verwandt≠ | 6 | 6 | 5 |
| Zusammenfassung≠ | 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. | Robust GLS extends classical Generalized Least Squares by pairing GLS coefficient estimation with heteroscedasticity- and autocorrelation-consistent (HAC) standard errors, or by using M-estimation within the GLS framework. It corrects for non-spherical errors — heteroscedasticity, autocorrelation, or both — while also guarding inference against misspecification of the error covariance structure. |
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