Relative entropy and spectral constraints: some invariance properties of the ARMA class

We determine the form of spectral densities of multidimensional scalar processes which minimize a relative entropy under a finite number of general moment-type constraints. The obtained theoretical results are applied to spectral densities of weakly stationary processes under covariances, inverse covariances and cepstral or impulse response constraints. Invariance properties of the class of autoregressive moving-average (ARMA) processes are shown to hold under the relative entropy minimization principle for many choices of entropy. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.