Legacy Documentation

Time Series (2011)

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1.2 Stationary Time Series Models

In this section the commonly used linear time series models (AR, MA, and ARMA models) are defined and the objects that represent them in Time Series are introduced. We outline the key concepts of weak stationarity and invertibility and state the conditions on the model parameters that ensure these properties. Functions that check for stationarity and invertibility of a given ARMA model and that expand a stationary model as an approximate MA model and an invertible model as an approximate AR model are then defined. We devote a considerable portion of the section to the discussion of the fundamental quantities, covariance, correlation, and partial correlation functions. We introduce and illustrate functions that calculate these quantities. Finally, we generalize the models and concepts to multivariate time series; all the functions defined in the univariate case can also be used for multivariate models as is demonstrated in a few examples.