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Moving-maximum models for extrema of time series

Hall, Peter, Peng, Liang and Yao, Qiwei (2002) Moving-maximum models for extrema of time series. Journal of Statistical Planning and Inference, 103 (1-2). pp. 51-63. ISSN 0378-3758

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Identification Number: 10.1016/S0378-3758(01)00197-5


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.

Item Type: Article
Official URL:
Additional Information: © 2002 Elsevier Science
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 26 Jun 2008 10:20
Last Modified: 20 May 2021 01:45

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