Linganisha mbinu

	Modelu Imara ya ARMA	Mfumo Imara wa Kujirejesha (Robust Autoregressive Model)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1986	1986
Mwanzilishi	Martin & Yohai (1986); broader robust time series literature	Martin & Yohai (influential early work); broader robust time series literature
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.	Martin, R. D., & Yohai, V. J. (1986). Influence functionals for time series. Annals of Statistics, 14(3), 781–818.
Majina mbadala	robust ARMA, outlier-robust ARMA, M-estimator ARMA, resistant ARMA estimation	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR
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 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.