Linganisha mbinu

	Muundo wa Wastani unaosikika (MA)	Modelu Imara ya ARMA
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1979–2009	1986
Mwanzilishi	Denby & Martin (1979); Muler, Pena & Yohai (2009)	Martin & Yohai (1986); broader robust time series literature
Aina	Robust time series model	Robust time series model
Chanzo asilia	Denby, L., & Martin, R. D. (1979). Robust estimation of the first-order autoregressive parameter. Journal of the American Statistical Association, 74(365), 140–146.	Franses, P. H., & Ghijsels, H. (1999). Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15(1), 1-9.
Majina mbadala	robust MA, robust moving average, M-estimation MA, bounded-influence MA	robust ARMA, outlier-robust ARMA, M-estimator ARMA, resistant ARMA estimation
Zinazohusiana	6	5
Muhtasari	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.	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.