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Moving-maximum models for extrema of time series

Hall, Peter; Peng, L; Yao, Qiwei

Description

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...[Show more]

dc.contributor.authorHall, Peter
dc.contributor.authorPeng, L
dc.contributor.authorYao, Qiwei
dc.date.accessioned2015-12-13T22:23:17Z
dc.identifier.issn0378-3758
dc.identifier.urihttp://hdl.handle.net/1885/72705
dc.description.abstractWe 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.
dc.publisherElsevier
dc.sourceJournal of Statistical Planning and Inference
dc.subjectKeywords: Autoregression; Bootstrap; Confidence interval; Extreme value distribution; Generalised pareto distribution; Moving average; Pareto distribution; Percentile method; Prediction interval
dc.titleMoving-maximum models for extrema of time series
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume103
dc.date.issued2002
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub3388
local.type.statusPublished Version
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationPeng, L, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationYao, Qiwei, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage51
local.bibliographicCitation.lastpage63
local.identifier.doi10.1016/S0378-3758(01)00197-5
dc.date.updated2015-12-11T08:04:33Z
local.identifier.scopusID2-s2.0-0037089915
CollectionsANU Research Publications

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