%0 Journal Article
%@ 0304-4149
%A Dahlhaus, Rainer
%C Amsterdam
%D 1996
%F heidok:20931
%I Elsevier
%J Stochastic processes and their applications
%K Locally stationary processes; Evolutionary spectra; Kullback-Leibler divergence; time varying autoregressions
%N 1
%P 139-168
%R 10.11588/heidok.00020931
%T On the Kullback-Leibler Information Divergence of LocallyStationary Processes
%U https://archiv.ub.uni-heidelberg.de/volltextserver/20931/
%V 62
%X A class of processes with a time varying spectral representationis introduced. A time varying spectral density is defined and a uniquenessproperty of this spectral density is established. As an example we study timevarying autoregressions. Several results on the asymptotic norm - andtrace behaviour of covariance matrices of such processes are derived. Asa consequence we prove a Kolmogorov formula for the local prediction error and calculate the asymptotic Kullback Leibler information divergence.