Properties of an Autoregressive Process

This section will examine the properties of an autoregressive process, AR(p), defined as 

The coefficients / , can be obtained by performing long division on the original polynomial expression given in Eq. (5.49). 

The mean value of the autoregressive process can be computed using Eq. (5.50), 

Clearly, if the series does not converge, then the mean value cannot exist. 

Theorem 5.2 Autocovariance of an Autoregressive Process. The autocovariance of an autoregressive process can be written as  

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