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

Author

Listed:
  • 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.

Suggested Citation

  • de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
  • Handle: RePEc:eee:spapps:v:32:y:1989:i:2:p:213-224
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