Derivation of the theoretical autocovariance and autocorrelation function of autoregessive moving average processes

Abstract

Closed form expressions for the theoretical autocovariance and autocorrelation function of mixed autoregressive moving average processes are presented. The results provide insight into the construction of autocovariances and autocorrelatians and are useful in theoretical analysis, model identification as well as in implementing maximum likelihood estimation algorithms.

Keywords:

• autoregressive moving average model
• auto covariance function
• autocorrelation function
• maximum likdlihood