قارن الطرق

	نموذج الانحدار الذاتي المتين	نموذج ARMA (متوسط متحرك ذاتي الانحدار)	الاسم المنهجي: المربعات الصغرى المعممة القوية (Robust GLS)
المجال	الاقتصاد القياسي	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1986	1970	1936 / 1980
صاحب الطريقة	Martin & Yohai (influential early work); broader robust time series literature	George E. P. Box and Gwilym M. Jenkins	Aitken (GLS theory, 1936); White (robust covariance, 1980)
النوع	Robust time series model	Time series model	Robust linear regression
المصدر التأسيسي	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.	Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson. Chapter 9: The Generalized Regression Model and Heteroscedasticity. ISBN: 978-0131395381
الأسماء البديلة	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	robust generalized least squares, GLS with robust standard errors, heteroscedasticity-consistent GLS, HC-GLS
ذات صلة	6	5	5
الملخص	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.	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.