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Autoregressive–moving-average model
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 auto-regression 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 1971 book by George E. P. Box and Gwilym Jenkins.
Given a time series of data ''X''''t'', the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The model is usually then referred to as the ARMA(''p'',''q'') model where ''p'' is the order of the autoregressive part and ''q'' is the order of the moving average part (as defined below).
== Autoregressive model ==
(詳細はparameters, is a constant, and the random variable is white noise.
Some constraints are necessary on the values of the parameters so that the model remains stationary. For example, processes in the AR(1) model with |''φ''1| ≥ 1 are not stationary.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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