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The Stationary Autogressive Model
STANFORD UNIV CA DEPT OF STATISTICS
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There are several ways of developing the autoregressive stochastic process as a finite-parameter model for time series analysis. This paper obtains the properties of the autoregressive process from a stationary stochastic process that satisfies the simple condition that a linear combination of current and past elements of the process is independent of or alternatively uncorrelated with all earlier elements of the process. This approach provides a coherent, clear, and rigorous exposition of the autoregressive model. The stationarity and independence imply that the roots of the associated polynomial equation are less than 1 in absolute value. The existence of the moving average representation is deduced and its form for distinct roots. The Yule-Walker equations, which are derived, determine the autocovariance sequence. Another set of parameters consists of the variance of the process and the partial autocorrelation sequence.
APPROVED FOR PUBLIC RELEASE