Computation of the autocovariances of stationary arma processes

Autoregressive-moving average (ARMA) models are often used for the purpose of forecasting a time series. As an aide to chosing a model, use is made of the autocorrelation function which is estimated from the data. If the only interest in the model is for forecasting purposes, then it is not necessary to compute the autocorrelation function associated with the chosen model. For this reason, a method for computation of the autocorrelation function is not usually included in the software used for identifying ARMA models. However, there are applications of ARMA models where it is important to compute the autocovariance function.

This paper contains an algorithm and a listing of a FORTRAN program which computes the autocovariance directly from the solution to the difference equations which govern its behavior.