Linganisha mbinu

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