قارن الطرق

	نموذج الانحدار الذاتي المتين	نموذج ARMA (متوسط متحرك ذاتي الانحدار)
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	1986	1970
صاحب الطريقة	Martin & Yohai (influential early work); broader robust time series literature	George E. P. Box and Gwilym M. Jenkins
النوع	Robust time series model	Time series model
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.
الأسماء البديلة	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)
ذات صلة	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 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.