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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


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]

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
Source: Journal of Applied Probability
DOI: 10.1239/jap/1091543413


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