השוואת שיטות

	מודל אוטורגרסיבי חסין (Robust Autoregressive Model)	מודל ARMA (אוטורגרסיבי ממוצע נע)	מודל אוטורגרסיבי (AR)	ריבועים פחותים מוכללים עמידים (Robust GLS)
תחום	אקונומטריקה	אקונומטריקה	אקונומטריקה	אקונומטריקה
משפחה	Regression model	Regression model	Regression model	Regression model
שנת המקור	1986	1970	1970s (popularised 1976)	1936 / 1980
הוגה השיטה	Martin & Yohai (influential early work); broader robust time series literature	George E. P. Box and Gwilym M. Jenkins	George E. P. Box and Gwilym M. Jenkins	Aitken (GLS theory, 1936); White (robust covariance, 1980)
סוג	Robust time series model	Time series model	Time series model	Robust linear regression
מקור מכונן	Martin, R. D., & Yohai, V. J. (1986). Influence functionals for time series. Annals of Statistics, 14(3), 781–818.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	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
כינויים	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	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
קשורות	6	5	6	5
תקציר	The robust AR model fits an autoregressive time series specification using estimation methods — typically M-estimators or bounded-influence estimators — that resist distortion from outliers and heavy-tailed error distributions. Unlike OLS-based AR estimation, robust variants down-weight extreme observations so that a small number of contaminated data points cannot dominate the fitted dynamics.	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.