On the relation between the maximum entropy probability density function and the autoregressive model

The problem of maximizing the entropy of an n-variate random vector subject to constraints on the first p + 1 autocovariance terms is examined. It is shown that the maximum is achieved by the Gaussian autoregressive process of order p satisfying the autocovariance constraints. This solution provides Burg's theorem about the maximum entropy spectral density as a special case.