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Article: Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors

TitleLimiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors
Authors
KeywordsBivariate Brownian Motion
Garch Models
Limiting Distribution
Maximum Likelihood Estimation
Stochastic Integral
Unstable Arma Models
Issue Date1998
Citation
Annals Of Statistics, 1998, v. 26 n. 1, p. 84-125 How to Cite?
AbstractThis paper investigates the maximum likelihood estimator (MLE) for unstable autoregressive moving-average (ARMA) time series with the noise sequence satisfying a general autoregressive heteroscedastic (GARCH) process. Under some mild conditions, it is shown that the MLE satisfying the likelihood equation exists and is consistent. The limiting distribution of the MLE is derived in a unified manner for all types of characteristic roots on or outside the unit circle and is expressed as a functional of stochastic integrals in terms of Brownian motions. For various types of unit roots, the limiting distribution of the MLE does not depend on the parameters in the moving-average component and hence, when the GARCH innovations reduce to usual white noises with a constant conditional variance, they are the same as those for the least squares estimators (LSE) for unstable autoregressive models given by Chan and Wei (1988). In the presence of the GARCH innovations, the limiting distribution will involve a sequence of independent bivariate Brownian motions with correlated components. These results are different from those already known in the literature and, in this case, the MLE of unit roots will be much more efficient than the ordinary least squares estimation.
Persistent Identifierhttp://hdl.handle.net/10722/172380
ISSN
2015 Impact Factor: 2.78
2015 SCImago Journal Rankings: 6.653
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLing, Sen_US
dc.contributor.authorLi, WKen_US
dc.date.accessioned2012-10-30T06:22:14Z-
dc.date.available2012-10-30T06:22:14Z-
dc.date.issued1998en_US
dc.identifier.citationAnnals Of Statistics, 1998, v. 26 n. 1, p. 84-125en_US
dc.identifier.issn0090-5364en_US
dc.identifier.urihttp://hdl.handle.net/10722/172380-
dc.description.abstractThis paper investigates the maximum likelihood estimator (MLE) for unstable autoregressive moving-average (ARMA) time series with the noise sequence satisfying a general autoregressive heteroscedastic (GARCH) process. Under some mild conditions, it is shown that the MLE satisfying the likelihood equation exists and is consistent. The limiting distribution of the MLE is derived in a unified manner for all types of characteristic roots on or outside the unit circle and is expressed as a functional of stochastic integrals in terms of Brownian motions. For various types of unit roots, the limiting distribution of the MLE does not depend on the parameters in the moving-average component and hence, when the GARCH innovations reduce to usual white noises with a constant conditional variance, they are the same as those for the least squares estimators (LSE) for unstable autoregressive models given by Chan and Wei (1988). In the presence of the GARCH innovations, the limiting distribution will involve a sequence of independent bivariate Brownian motions with correlated components. These results are different from those already known in the literature and, in this case, the MLE of unit roots will be much more efficient than the ordinary least squares estimation.en_US
dc.languageengen_US
dc.relation.ispartofAnnals of Statisticsen_US
dc.subjectBivariate Brownian Motionen_US
dc.subjectGarch Modelsen_US
dc.subjectLimiting Distributionen_US
dc.subjectMaximum Likelihood Estimationen_US
dc.subjectStochastic Integralen_US
dc.subjectUnstable Arma Modelsen_US
dc.titleLimiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errorsen_US
dc.typeArticleen_US
dc.identifier.emailLi, WK: hrntlwk@hku.hken_US
dc.identifier.authorityLi, WK=rp00741en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0032399852en_US
dc.identifier.hkuros31339-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0032399852&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume26en_US
dc.identifier.issue1en_US
dc.identifier.spage84en_US
dc.identifier.epage125en_US
dc.identifier.isiWOS:000079135300003-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLing, S=7102701223en_US
dc.identifier.scopusauthoridLi, WK=14015971200en_US

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