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Prediction and nonparametric estimation for time series analysis with heavy tails

Hall, Peter; Peng, L; Yao, Qiwei

Description

Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on 'local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional 'local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares...[Show more]

dc.contributor.authorHall, Peter
dc.contributor.authorPeng, L
dc.contributor.authorYao, Qiwei
dc.date.accessioned2015-12-13T22:23:17Z
dc.date.available2015-12-13T22:23:17Z
dc.identifier.issn0143-9782
dc.identifier.urihttp://hdl.handle.net/1885/72707
dc.description.abstractMotivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on 'local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional 'local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance.
dc.publisherBlackwell Publishing Ltd
dc.sourceJournal of Time Series Analysis
dc.subjectKeywords: ?-mixing; ARMA model; Conditional median; Heavy tail; Least absolute deviation estimation; Local-linear regression; Prediction; Regular variation; Stable distribution; Strong mixing; Time series analysis
dc.titlePrediction and nonparametric estimation for time series analysis with heavy tails
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume23
dc.date.issued2002
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub3389
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.bibliographicCitation.issue3
local.bibliographicCitation.startpage313
local.bibliographicCitation.lastpage331
local.identifier.doi10.1111/1467-9892.00266
dc.date.updated2015-12-11T08:04:34Z
local.identifier.scopusID2-s2.0-0040080056
CollectionsANU Research Publications

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