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Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes

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Author Info

  • de Haan, Laurens
  • Resnick, Sidney I.
  • Rootzén, Holger
  • de Vries, Casper G.

Abstract

We consider limit distributions of extremes of a process {Yn} satisfying the stochastic difference equation Yn-AnYn-1+Bn, n[greater-or-equal, slanted]1,Y0[greater-or-equal, slanted]0, where {An, Bn} are i.i.d. 2+-valued random pairs, A special case of interest is when {Yn} is derived from a first order ARCH process. Parameters of the limit law are exhibited; some are hard to calculate explicitly but easy to simulate.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 32 (1989)
Issue (Month): 2 (August)
Pages: 213-224

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Handle: RePEc:eee:spapps:v:32:y:1989:i:2:p:213-224

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Related research

Keywords: extreme values ARCH process stochastic difference equation with random coefficients;

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