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AuthorBrandes, Dirk-Philipdc.contributor.author
Date of accession2018-08-24T12:47:47Zdc.date.accessioned
Available in OPARU since2018-08-24T12:47:47Zdc.date.available
Year of creation2018dc.date.created
Date of first publication2018-08-24dc.date.issued
AbstractThis thesis covers miscellaneous topics in the field of time series analysis and stochastic processes and consists of four topics where the first two are connected by the appearance of random coefficients and the last two by inference of Lévy driven continuous time moving average processes. In Chapter 2, we consider a random recurrence equation driven by a bivariate i.i.d. sequence. Much attention has been paid to causal strictly stationary solutions of that random recurrence equation, i.e. to strictly stationary solutions of this equation when the start variable is assumed to be independent of the driving sequence. For this case, a complete characterization when such causal solutions exist can be found in literature. We shall dispose of the independence assumption and derive necessary and sufficient conditions for a strictly stationary, not necessarily causal solution of this equation to exist. In Chapter 3, we introduce a continuous time autoregressive moving average process with random Lévy coefficients, termed RC-CARMA(p,q) process, of order p and q < p via a subclass of multivariate generalized Ornstein-Uhlenbeck processes. Sufficient conditions for the existence of a strictly stationary solution and the existence of moments are obtained. We further investigate second order stationarity properties, calculate the auto- covariance function and spectral density, and give sufficient conditions for their existence. In Chapter 4, we study a Lévy driven continuous time moving average process X sampled at random times which follow a renewal structure independent of X. Asymptotic normality of the sample mean, the sample autocovariance, and the sample autocorrelation is established under certain conditions on the kernel and the random times. We compare our results to a classical non-random equidistant sampling method and give an application to parameter estimation of the Lévy driven Ornstein-Uhlenbeck process. As an extension of the results in Chapter 4, we consider in Chapter 5 multivariate Lévy driven continuous time moving average processes X. We first sample the process X at a non-random equidistant sequence and establish the asymptotic normality of the sample mean. Secondly, we use a renewal sampling sequence independent of X and derive also in this case the asymptotic normality of the sample mean.dc.description.abstract
Languageen_USdc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
KeywordCARMA processesdc.subject
KeywordContinuous time autoregressive moving average processesdc.subject
KeywordSample meandc.subject
KeywordSample autocorrelationdc.subject
KeywordSample autocovariancedc.subject
KeywordRenewal samplingdc.subject
KeywordRandom coefficientsdc.subject
KeywordMultivariate generalized Ornstein-Uhlenbeck processdc.subject
KeywordStationaritydc.subject
KeywordNon-anticipativedc.subject
KeywordRandom recurrence equationdc.subject
KeywordStrictly stationarydc.subject
KeywordSecond order stationaritydc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHMoving averagesdc.subject.lcsh
LCSHCentral limit theoremdc.subject.lcsh
LCSHLévy processesdc.subject.lcsh
LCSHAutocorrelation (Statistics)dc.subject.lcsh
LCSHOrnstein-Uhlenbeck processdc.subject.lcsh
TitleCARMA models with random coefficients and inference for renewal sampled Lévy driven moving average processesdc.title
Resource typeDissertationdc.type
Date of acceptance2018-07-26dcterms.dateAccepted
RefereeLindner, Alexanderdc.contributor.referee
RefereeBehme, Anitadc.contributor.referee
DOIhttp://dx.doi.org/10.18725/OPARU-9247dc.identifier.doi
PPN1030031576dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-oparu-9304-4dc.identifier.urn
GNDMA-Prozessdc.subject.gnd
GNDZentraler Grenzwertsatzdc.subject.gnd
GNDLévy-Prozessdc.subject.gnd
GNDAutokorrelationdc.subject.gnd
GNDOrnstein-Uhlenbeck-Prozessdc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
InstitutionInstitut für Finanzmathematikuulm.affiliationSpecific
Grantor of degreeFakultät für Mathematik und Wirtschaftswissenschaftenuulm.thesisGrantor
DCMI TypeTextuulm.typeDCMI
CategoryPublikationenuulm.category


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