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Statistical modeling with COGARCH(p,q) processes

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dc.contributor.authorChadraa, Erdenebaatar, author
dc.contributor.authorBrockwell, Peter J., advisor
dc.date.accessioned2024-03-13T18:50:57Z
dc.date.available2024-03-13T18:50:57Z
dc.date.issued2009
dc.description.abstractIn this paper, a family of continuous time GARCH processes, generalizing the COGARCH(1, 1) process of Klüppelberg, et al. (2004), is introduced and studied. The resulting COGARCH(p,q) processes, q ≥ p ≥ 1, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than those of the COGARCH(1, 1) process. We establish sufficient conditions for the existence of a strictly stationary non-negative solution of the equations for the volatility process and, under conditions which ensure the finiteness of the required moments, determine the autocorrelation functions of both the volatility and squared increment processes. The volatility process is found to have the autocorrelation function of a continuous-time ARMA process while the squared increment process has the autocorrelation function of an ARMA process.
dc.description.abstractTo estimate the parameters of the COGARCH(2, 2) processes, the least-squares method is used. We give conditions under which the volatility and the squared increment processes are strongly mixing, from which it follows that the least-squares estimators are strongly consistent and asymptotically normal. Finally, the model is fitted to a high frequency dataset.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Chadraa_2009_3400988.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237634
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectGARCH processes
dc.subjectleast-squares estimators
dc.subjectvolatility process
dc.subjectstatistics
dc.subjectfinance
dc.subjectapplied mathematics
dc.titleStatistical modeling with COGARCH(p,q) processes
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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