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Parameter estimation in nonlinear AR-GARCH models

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dc.contributor.coauthorSaikkonen, Pentti
dc.contributor.departmentDepartment of Economics
dc.contributor.kuauthorMeitz, Mika
dc.contributor.schoolcollegeinstituteCollege of Administrative Sciences and Economics
dc.date.accessioned2024-11-09T23:36:58Z
dc.date.issued2011
dc.description.abstractThis paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue6
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipAcademy of Finland
dc.description.sponsorshipFinnish Foundation for the Advancement of Securities Markets
dc.description.sponsorshipOP-Pohjola Group Research Foundation
dc.description.sponsorshipYrjo Jahnsson Foundation
dc.description.sponsorshipDanish National Research Foundation
dc.description.sponsorshipEuropean University Institute We acknowledge financial support from the Academy of Finland (PS), the Finnish Foundation for the Advancement of Securities Markets (MM), OP-Pohjola Group Research Foundation (MM and PS), and the Yrjo Jahnsson Foundation (MM and PS). We thank a co-editor and two anonymous referees for helpful comments and suggestions. The first version of this paper was completed in May 2008 while the first author was a post-doctoral research fellow at University of Oxford's Department of Economics. Parts of this research were also carried out while the first author was visiting the Center for Research in Econometric Analysis of Time Series (CREATES) at University of Aarhus (funded by the Danish National Research Foundation) and during the second author's Fernand Braudel Fellowship at the European University Institute. Both institutions are thanked for their hospitality. Material from the paper has been presented at the Second Brussels-Waseda Seminar on Time Series and Financial Statistics, Brussels, June 2008
dc.description.sponsorshipESRC Econometric Study Group Annual Conference, Bristol, July 2008
dc.description.sponsorshipWorkshop on Nonparametric Function Estimation with Applications in Finance, Oulu, June 2009
dc.description.sponsorshipEconometrics, Time Series Analysis and Systems Theory-A Conference in Honor of Manfred Deistler, Vienna, June 2009
dc.description.sponsorship64th European Meeting of the Econometric Society, Barcelona, August 2009
dc.description.sponsorshipInternational Symposium on Econometric Theory and Applications, Singapore, April 2010
dc.description.sponsorshipand in seminars at Bilkent University, Graz University of Technology, Koc, University, University of Aarhus, and University of Vienna. We thank the participants in these occasions for their comments. Address correspondence to: Mika Meitz, Department of Economics, Koc, University, Rumelifeneri Yolu, 34450 Sariyer, İstanbul, Turkey
dc.description.sponsorshipe-mail: mmeitz@ku.edu.tr
dc.description.sponsorshipor to: Pentti Saikkonen, Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 University of Helsinki, Finland
dc.description.sponsorshipe-mail: pentti.saikkonen@helsinki.fi.
dc.description.volume27
dc.identifier.doi10.1017/S0266466611000041
dc.identifier.eissn1469-4360
dc.identifier.issn0266-4666
dc.identifier.quartileQ4
dc.identifier.scopus2-s2.0-82455212337
dc.identifier.urihttps://doi.org/10.1017/S0266466611000041
dc.identifier.urihttps://hdl.handle.net/20.500.14288/12751
dc.identifier.wos297637500004
dc.keywordsMaximum-likelihood-estimation
dc.keywordsAverage time-series
dc.keywordsAutoregressive models
dc.keywordsConditional heteroscedasticity
dc.keywordsAsymptotic theory
dc.language.isoeng
dc.publisherCambridge Univ Press
dc.relation.ispartofEconometric Theory
dc.subjectEconomics
dc.subjectMathematics
dc.subjectSocial Sciences
dc.subjectMathematical methods
dc.subjectStatistics
dc.subjectProbability
dc.titleParameter estimation in nonlinear AR-GARCH models
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMeitz, Mika
local.publication.orgunit1College of Administrative Sciences and Economics
local.publication.orgunit2Department of Economics
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