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

@article{Klppelberg2004ACG, title={A continuous-time GARCH process driven by a L{\'e}vy process: stationarity and second-order behaviour}, author={Claudia Kl{\"u}ppelberg and Alexander M. Lindner and Ross A. Maller}, journal={Journal of Applied Probability}, year={2004}, volume={41}, pages={601 - 622} }

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…

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