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On the Kullback-Leibler information divergence of locally stationary processes

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  • Dahlhaus, R.

Abstract

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.

Suggested Citation

  • Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    • Handle: RePEc:eee:spapps:v:62:y:1996:i:1:p:139-168
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    References listed on IDEAS

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    1. Marc Hallin, 1986. "Nonstationary q-dependent processes and time-varying moving average models: invertibility properties and the forecasting problem," ULB Institutional Repository 2013/2005, ULB -- Universite Libre de Bruxelles.
    2. Guy Mélard & Annie Herteleer‐de Schutter, 1989. "Contributions To Evolutionary Spectral Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(1), pages 41-63, January.
    3. Hallin, Marc, 1978. "Mixed autoregressive-moving average multivariate processes with time-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 567-572, December.
    4. Guy Melard & Annie Herteleer, 1989. "Contributions to the evolutionary spectral theory," ULB Institutional Repository 2013/13708, ULB -- Universite Libre de Bruxelles.
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