Linganisha mbinu

	Mfumo Imara wa Kujirejesha (Robust Autoregressive Model)	Modeli ya ARMA (Autoregressive Moving Average)	Muundo wa Autoregressive (AR)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1986	1970	1970s (popularised 1976)
Mwanzilishi	Martin & Yohai (influential early work); broader robust time series literature	George E. P. Box and Gwilym M. Jenkins	George E. P. Box and Gwilym M. Jenkins
Aina	Robust time series model	Time series model	Time series model
Chanzo asilia	Martin, R. D., & Yohai, V. J. (1986). Influence functionals for time series. Annals of Statistics, 14(3), 781–818.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043
Majina mbadala	robust autoregression, outlier-robust AR, M-estimator AR, heavy-tail AR	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	AR model, AR(p) model, autoregression, AR process
Zinazohusiana	6	5	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.	The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting.	An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial series.