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Lithuanian Mathematical Journal

, Volume 47, Issue 2, pp 164–175 | Cite as

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

  • A. Klivečka
  • D. Surgailis
Article

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.

Keywords

GARCH(1,1) process tail index heavy-tailed distributions 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. Klivečka
    • 1
  • D. Surgailis
    • 2
  1. 1.Vilnius UniversityLT-VilniusLithuania
  2. 2.Institute of Mathematics and InformaticsVilniusLithuania

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