A simple set of linear equations for computing autocorrelations of ARMA(p,q) signals with given model parameters

A new formulation facilitating the determination of the autocorrelation lags, and consequently the autocorrelation matrix, of an autoregressive moving average signal of arbitrary order (ARMA(p, q)) is presented. The main features of our formulation, stated as a set of linear equations to be solved, are 1) its conceptual simplicity 2) its reliance only on primary parameters of the ARMA(p, q) model, and 3) the simplicity of the resulting linear equations.