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On the Kullback-Leibler Information Divergence of LocallyStationary Processes

Dahlhaus, Rainer

In: Stochastic processes and their applications, 62 (1996), Nr. 1. pp. 139-168. ISSN 0304-4149

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Abstract

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.

Item Type: Article
Journal or Publication Title: Stochastic processes and their applications
Volume: 62
Number: 1
Publisher: Elsevier
Place of Publication: Amsterdam
Date Deposited: 13 Jun 2016 08:50
Date: 1996
ISSN: 0304-4149
Page Range: pp. 139-168
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Locally stationary processes; Evolutionary spectra; Kullback-Leibler divergence; time varying autoregressions
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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