Computing of autocorrelation of time processes based on power series

There are several ways to compute the autocorrelation and autocovariance matrixs of causal ARMA(p, q) process[1], The multiple time series analysis[2] shows that the computing process is very complicated in the multiple cases, in practice, with the backward shift operator, the autoregressive operator and moving average operator, time series can be transformed into polynomial which are usually related to the power series, in this paper, we demonstrate the approaches to use the geometrics series to compute autocorrelation function.