On the maximal entropy property for ARMA processes and ARMA approximation

The existence and properties of a general ARMA (p, q) process, whose autocovariances, up to lag p, and impulse coefficients, up to lag q, coincide with some given values, are shown. A closed-form solution is obtained. Based on this, the maximal entropy property for ARMA process and the relation and difference between ARMA maximal entropy approximation and extended Padé approximation are discussed. This method may be used for the design of digital filters and for ARMA spectral estimation.