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

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

Stochastic Processes and their Applications, 1989, vol. 32, issue 2, 213-224

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.

Keywords: extreme; values; ARCH; process; stochastic; difference; equation; with; random; coefficients (search for similar items in EconPapers)
Date: 1989
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