قارن الطرق

	نموذج الانحدار الذاتي المتين	نموذج ARIMA (الانحدار الذاتي المتكامل المتوسط المتحرك)	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 Box and Gwilym Jenkins	Aitken (GLS theory, 1936); White (robust covariance, 1980)
النوع	Robust time series model	Time series forecasting 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	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	robust generalized least squares, GLS with robust standard errors, heteroscedasticity-consistent GLS, HC-GLS
ذات صلة	6	6	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 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.	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.