NDLI: A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour

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A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour

Content Provider	Scilit
Author	Klüppelberg, Claudia Lindner, Alexander Maller, Ross
Copyright Year	2004
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 discrete-time GARCH processes, and is amenable to further analysis, possessing useful Markovian and stationarity properties.
Related Links	https://epub.ub.uni-muenchen.de/1794/1/paper_425.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FD2A5B8B09E33236ED272997E37C54A1/S0021900200020428a.pdf/div-class-title-a-continuous-time-garch-process-driven-by-a-levy-process-stationarity-and-second-order-behaviour-div.pdf
Ending Page	622
Page Count	22
Starting Page	601
ISSN	00219002
e-ISSN	14756072
DOI	10.1017/s0021900200020428
Journal	Journal of applied probability
Issue Number	03
Volume Number	41
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2004-09-01
Access Restriction	Open
Subject Keyword	Journal of applied probability Mathematical Physics Conditional Heteroscedasticity Stochastic Integration
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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