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| Modello ARMA (Autoregressive Moving Average)× | Modello Autoregressivo (AR)× | Robust Generalized Least Squares (Robust GLS)× | |
|---|---|---|---|
| Campo | Econometria | Econometria | Econometria |
| Famiglia | Regression model | Regression model | Regression model |
| Anno di origine≠ | 1970 | 1970s (popularised 1976) | 1936 / 1980 |
| Ideatore≠ | George E. P. Box and Gwilym M. Jenkins | George E. P. Box and Gwilym M. Jenkins | Aitken (GLS theory, 1936); White (robust covariance, 1980) |
| Tipo≠ | Time series model | Time series model | Robust linear regression |
| 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 | Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson. Chapter 9: The Generalized Regression Model and Heteroscedasticity. ISBN: 978-0131395381 |
| Alias | ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q) | AR model, AR(p) model, autoregression, AR process | robust generalized least squares, GLS with robust standard errors, heteroscedasticity-consistent GLS, HC-GLS |
| 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. | 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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