Abstract
We consider general nonstationary max-autoregressive sequences X i , i ⩾ 1, with X i = Z i max( X i − 1 , Y i ) where Y i , i ⩾ 1 is a sequence of i.i.d. random variables and Z i , i ⩾ 1 is a sequence of independent random variables (0 ⩽ Z i ⩽ 1), independent of Y i . We deal with the limit law of extreme values M n = max X i , i ⩽ n (as n → ∞) and evaluate the extremal index for the case where the marginal distribution of Y i is regularly varying at ∞. The limit of the point process of exceedances of a boundary u n by X i , i ⩽ n, is derived (as n → ∞) by analysing the convergence of the cluster distribution and of the intensity measure.
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