Title of article
Extremal behavior of the autoregressive process with ARCH(1) errors
Author/Authors
Borkovec، نويسنده , , Milan، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2000
Pages
19
From page
189
To page
207
Abstract
We investigate the extremal behavior of a special class of autoregressive processes with ARCH(1) errors given by the stochastic difference equationXn=αXn−1+β+λXn−12εn, n∈N,where (εn)n∈N 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
compound Poisson process , Extremal behavior , Extremal index , Fréchet distribution , Heavy tail , Heteroscedastic homogeneous Markov process , Separating sequence , Recurrent Harris chain , ARCH Model , Autoregressive process , strong mixing , Coupling
Journal title
Stochastic Processes and their Applications
Serial Year
2000
Journal title
Stochastic Processes and their Applications
Record number
1576592
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