Linganisha mbinu

	Mfumo Imara wa Kujirejesha (Robust Autoregressive Model)	OLS Imara (OLS yenye Makosa Sanifu Imara)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1986	1980
Mwanzilishi	Martin & Yohai (influential early work); broader robust time series literature	Halbert White
Aina	Robust time series model	Linear regression with robust inference
Chanzo asilia	Martin, R. D., & Yohai, V. J. (1986). Influence functionals for time series. Annals of Statistics, 14(3), 781–818.	White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.
Majina mbadala	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	HC robust regression, White robust OLS, sandwich estimator OLS, OLS with robust standard errors
Zinazohusiana	6	6
Muhtasari	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.	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.