مقایسهٔ روش‌ها

	مدل میانگین متحرک قوی (MA)	مدل آریما مقاوم (Robust ARIMA)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1979–2009	1986–1993
پدیدآور	Denby & Martin (1979); Muler, Pena & Yohai (2009)	Tsay (1986); Chen & Liu (1993)
نوع	Robust time series model	Robust time series model
منبع بنیادین	Denby, L., & Martin, R. D. (1979). Robust estimation of the first-order autoregressive parameter. Journal of the American Statistical Association, 74(365), 140–146.	Tsay, R. S. (1986). Time series model specification in the presence of outliers. Journal of the American Statistical Association, 81(393), 132–141.
نام‌های دیگر	robust MA, robust moving average, M-estimation MA, bounded-influence MA	robust ARIMA, outlier-resistant ARIMA, robust time series estimation, ARIMA with outlier detection
مرتبط	6	4
خلاصه	The Robust MA model applies robust estimation — typically M-estimation or bounded-influence methods — to the Moving Average time series model. By replacing the ordinary least squares loss with a bounded loss function, it produces parameter estimates that are far less sensitive to outliers, additive noise spikes, or heavy-tailed error distributions than the classical Gaussian MA.	Robust ARIMA extends the classical ARIMA framework to detect and correct the influence of outliers and structural breaks during estimation. By jointly identifying anomalous observations and re-estimating model parameters, it produces coefficient estimates and forecasts that are far less distorted by isolated shocks or data errors than standard ARIMA.