Computing the Autocorrelation Function for the Autoregressive Process

In this document, we explain how complex integration theory can be used to compute the autocorrelation function for the autoregressive process. In particular, we use the deformation invariance theorem, and Cauchy’s residue theorem to reduce the problem of computing the autocorrelation function to the problem of computing residues of a particular function. The purpose of this paper is not only to illustrate a method by which one can derive the autocorrelation function of the autoregressive process, but also to demonstrate the applicability of complex analysis in statistical theory through simple examples.