Linganisha mbinu

	Modelu Imara ya ARMA	OLS Imara (OLS yenye Makosa Sanifu Imara)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1986	1980
Mwanzilishi	Martin & Yohai (1986); broader robust time series literature	Halbert White
Aina	Robust time series model	Linear regression with robust inference
Chanzo asilia	Franses, P. H., & Ghijsels, H. (1999). Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15(1), 1-9.	White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.
Majina mbadala	robust ARMA, outlier-robust ARMA, M-estimator ARMA, resistant ARMA estimation	HC robust regression, White robust OLS, sandwich estimator OLS, OLS with robust standard errors
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.	Robust OLS applies ordinary least squares to estimate coefficients and then replaces the classical standard errors with heteroscedasticity-consistent (HC) standard errors — commonly called White standard errors. This leaves the point estimates unchanged while yielding valid t-statistics and confidence intervals even when the error variance is not constant across observations.