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

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Date

2004

Authors

Kluppelberg, Claudia
Lindner, Alexander
Maller, Ross

Journal Title

Journal ISSN

Volume Title

Publisher

Applied Probability Trust

Abstract

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.

Description

Keywords

Keywords: ARCH model; Conditional heteroscedasticity; GARCH model; Lévy process; Perpetuities; Stability; Stationarity; Stochastic integration

Citation

URI

http://hdl.handle.net/1885/80909

Collections

ANU Research Publications

Source

Journal of Applied Probability

Type

Journal article

Book Title

Entity type

Access Statement

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DOI

10.1239/jap/1091543413

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