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.

Author Bio

Omar Talib will be graduating with a BSc in statistics this year. After his graduation, he shall apply for a graduate program in pure mathematics and is hoping to get a Ph.D. in algebraic topology. He spends most of his free time studying mathematics and philosophy. He also enjoys having long walks and listening to classical music, especially the music of Bach, Brahms and Beethoven.

Souleimane Cheikh Sidi Mohamed is student at the Modern College of Business and Science majoring in statistics. In his free time, he likes to write computer programs and learn new things about computers in general. He also enjoys reading mathematics, traveling and meeting people.