On the Kullback-Leibler information divergence of locally stationary processes

A class of processes with a time varying spectral representation is established. As an example we study time varying autoregressions. Several results on the asymptotic norm behaviour and trace behaviour of covariance matrices of such processes are derived. As a consequence we prove a Kolmogorov formula for the local prediction error and calculate the asymptotic Kullback-Leibler information divergence.