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An example of a linear time series model is an [[autoregressive moving average model]]. Here the model for values {''X<sub>t</sub>''} in a time series can be written in the form
:<math> X_t = c + \varepsilon_t + \sum_{i=1}^p \
where again the quantities ''ε<sub>t</sub>'' are random variables representing [[Innovation (signal processing)|innovations]] which are new random effects that appear at a certain time but also affect values of ''X'' at later times. In this instance the use of the term "linear model" refers to the structure of the above relationship in representing ''X<sub>t</sub>'' as a linear function of past values of the same time series and of current and past values of the innovations.<ref>Priestley, M.B. (1988) ''Non-linear and Non-stationary time series analysis'', Academic Press. ISBN 0-12-564911-8</ref> This particular aspect of the structure means that it is relatively simple to derive relations for the mean and [[covariance]] properties of the time series. Note that here the "linear" part of the term "linear model" is not referring to the coefficients ''φ<sub>i</sub>'' and ''θ<sub>i</sub>'', as it would be in the case of a regression model, which looks structurally similar.
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