قارن الطرق

	نموذج ARMA المتين	نموذج ARIMA (الانحدار الذاتي المتكامل المتوسط المتحرك)
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	1986	1970
صاحب الطريقة	Martin & Yohai (1986); broader robust time series literature	George Box and Gwilym Jenkins
النوع	Robust time series model	Time series forecasting model
المصدر التأسيسي	Franses, P. H., & Ghijsels, H. (1999). Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15(1), 1-9.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
الأسماء البديلة	robust ARMA, outlier-robust ARMA, M-estimator ARMA, resistant ARMA estimation	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)
ذات صلة	5	6
الملخص	The Robust ARMA model extends the classical Autoregressive Moving Average framework by replacing the sensitive least-squares loss with outlier-resistant estimation methods — typically M-estimators or median-based approaches. This protects coefficient estimates and forecasts from being distorted by additive outliers, level shifts, or innovational outliers that are common in economic and financial time series.	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.