Extremal behavior of the autoregressive process with ARCH(1) errors

Milan Borkovec

Stochastic Processes and their Applications, 2000, vol. 85, issue 2, 189-207

Abstract: We investigate the extremal behavior of a special class of autoregressive processes with ARCH(1) errors given by the stochastic difference equationwhere are i.i.d. random variables. The extremes of such processes occur typically in clusters. We give an explicit formula for the extremal index and the probabilities for the length of a cluster.

Keywords: ARCH; model; Autoregressive; process; Compound; Poisson; process; Coupling; Extremal; behavior; Extremal; index; Frechet; distribution; Heavy; tail; Heteroscedastic; homogeneous; Markov; process; Recurrent; Harris; chain; Separating; sequence; Strong; mixing (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (8)

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