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A continous-time GARCH process driven by a Levy process: stationarity and second-order behaviour

Kluppelberg, Claudia; Lindner, Alexander; Maller, Ross

Description

We use a discrete-time analysis, giving necessary and sufficient conditions for the almost-sure convergence of ARCH(1) and GARCH(1, 1) discrete-time models, to suggest an extension of the ARCH and GARCH concepts to continuous-time processes. Our 'COGARCH' (continuous-time GARCH) model, based on a single background driving Lévy process, is different from, though related to, other continuous-time stochastic volatility models that have been proposed. The model generalises the essential features of...[Show more]

dc.contributor.authorKluppelberg, Claudia
dc.contributor.authorLindner, Alexander
dc.contributor.authorMaller, Ross
dc.date.accessioned2015-12-13T22:50:42Z
dc.date.available2015-12-13T22:50:42Z
dc.identifier.issn0021-9002
dc.identifier.urihttp://hdl.handle.net/1885/80909
dc.description.abstractWe use a discrete-time analysis, giving necessary and sufficient conditions for the almost-sure convergence of ARCH(1) and GARCH(1, 1) discrete-time models, to suggest an extension of the ARCH and GARCH concepts to continuous-time processes. Our 'COGARCH' (continuous-time GARCH) model, based on a single background driving Lévy process, is different from, though related to, other continuous-time stochastic volatility models that have been proposed. The model generalises the essential features of discrete-time GARCH processes, and is amenable to further analysis, possessing useful Markovian and stationarity properties.
dc.publisherApplied Probability Trust
dc.sourceJournal of Applied Probability
dc.subjectKeywords: ARCH model; Conditional heteroscedasticity; GARCH model; Lévy process; Perpetuities; Stability; Stationarity; Stochastic integration
dc.titleA continous-time GARCH process driven by a Levy process: stationarity and second-order behaviour
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume41
dc.date.issued2004
local.identifier.absfor010406 - Stochastic Analysis and Modelling
local.identifier.ariespublicationMigratedxPub9214
local.type.statusPublished Version
local.contributor.affiliationKluppelberg, Claudia, Munich University of Technology
local.contributor.affiliationLindner, Alexander, Munich University of Technology
local.contributor.affiliationMaller, Ross, College of Business and Economics, ANU
local.bibliographicCitation.startpage601
local.bibliographicCitation.lastpage622
local.identifier.doi10.1239/jap/1091543413
dc.date.updated2015-12-11T10:41:56Z
local.identifier.scopusID2-s2.0-10244257719
CollectionsANU Research Publications

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