Linganisha mbinu

	Muundo wa Wastani unaosikika (MA)	Modeli ya ARMA (Autoregressive Moving Average)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1979–2009	1970
Mwanzilishi	Denby & Martin (1979); Muler, Pena & Yohai (2009)	George E. P. Box and Gwilym M. Jenkins
Aina	Robust time series model	Time series model
Chanzo asilia	Denby, L., & Martin, R. D. (1979). Robust estimation of the first-order autoregressive parameter. Journal of the American Statistical Association, 74(365), 140–146.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Majina mbadala	robust MA, robust moving average, M-estimation MA, bounded-influence MA	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)
Zinazohusiana	6	5
Muhtasari	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.	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.