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Garch(1,1) process can have arbitrarily heavy power tails

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Abstract

We study the structure of solutions of Kesten’s equation (1.5), where a, b ⩾ 0 are the coefficients of the GARCH(1,1) process in (1.1). We prove that, for any b ∈ (0, 1) and any κ > 0 small enough, there exists a stationary GARCH(1,1) process with tail index κ.

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Authors and Affiliations

  1. Vilnius University, Naugarduko 24, 03225, LT-Vilnius, Lithuania

    A. Klivečka

  2. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania

    D. Surgailis

Authors
  1. A. Klivečka
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  2. D. Surgailis
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Additional information

The research was partially supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation, grant no. T-15/07.

Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 196–210, April–June, 2007.

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Klivečka, A., Surgailis, D. Garch(1,1) process can have arbitrarily heavy power tails. Lith Math J 47, 164–175 (2007). https://doi.org/10.1007/s10986-007-0012-z

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  • DOI: https://doi.org/10.1007/s10986-007-0012-z

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