Moving-maximum models for extrema of time series

Peter Hall, Liang Peng and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We discuss moving-maximum models, based on weighted maxima of independent random variables, for extreme values from a time series. The models encompass a range of stochastic processes that are of interest in the context of extreme-value data. We show that a stationary stochastic process whose finite-dimensional distributions are extreme-value distributions may be approximated arbitrarily closely by a moving-maximum process with extreme-value marginals. It is demonstrated that bootstrap techniques, applied to moving-maximum models, may be used to construct confidence and prediction intervals from dependent extrema. Moreover, it is shown that bootstrapped moving-maximum models may be used to capture the dominant features of a range of processes that are not themselves moving maxima. Connections of moving-maximum models to more conventional, moving-average processes are addressed. In particular, it is proved that a moving-maximum process with extreme-value distributed marginals may be approximated by powers of moving-average processes with stably distributed marginals.

Keywords: autoregression; bootstrap; confidence interval; extreme value distribution; generalised pareto distribution; moving average; Pareto distribution; percentile method; prediction interval (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2002-04-15
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Citations: View citations in EconPapers (9)

Published in Journal of Statistical Planning and Inference, 15, April, 2002, 103(1-2), pp. 51-63. ISSN: 0378-3758

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:6084

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