Video encyclopedia

Autoregressive–moving-average model


Autoregressive vs Moving Average Order One processes - part 1


Mean of ARMA Model


Autoregressive Moving-Average Generator


R Tutorial : Stationary Time Series: ARMA


Autoregressive Moving-Average Simulation (First Order)

In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression and the second for the moving average. The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins.
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    • Autoregressive model 

    • Moving-average model 

    • ARMA model 

    • Note about the error terms 

    • Specification in terms of lag operator 

    • Fitting models 

    • Applications 

    • Generalizations