Extremes and clustering of nonstationary max-AR(1) sequences

M. T. Alpuim, N. A. Catkan and J. Hüsler

Stochastic Processes and their Applications, 1995, vol. 56, issue 1, 171-184

Abstract: We consider general nonstationary max-autoregressive sequences Xi, i [greater-or-equal, slanted] 1, with Xi = Zimax(Xi - 1, Yi) where Yi, i [greater-or-equal, slanted] 1 is a sequence of i.i.d. random variables and Zi, i [greater-or-equal, slanted] 1 is a sequence of independent random variables (0 [less-than-or-equals, slant] Zi [less-than-or-equals, slant] 1), independent of Yi. We deal with the limit law of extreme values Mn = maxXi, i [less-than-or-equals, slant] n (as n --> [infinity]) and evaluate the extremal index for the case where the marginal distribution of Yi is regularly varying at [infinity]. The limit of the point process of exceedances of a boundary un by Xi, i [less-than-or-equals, slant] n, is derived (as n --> [infinity]) by analysing the convergence of the cluster distribution and of the intensity measure.

Keywords: Nonstationary; Extreme; values; Point; processes; Regular; variation; Weak; limits; Max-autoregressive; sequences (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (1)

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