Stationarity and second order behaviour of discrete and continuous time GARCH(1,1) processes

Klüppelberg, Claudia; Lindner, Alexander M. und Maller, R. A. (2003): Stationarity and second order behaviour of discrete and continuous time GARCH(1,1) processes. Sonderforschungsbereich 386, Discussion Paper 337

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 (G)ARCH concept to continuous time processes. The models, based on a single background driving Levy process, are different from, though related to, other continuous time stochastic volatility models that have been proposed. Our models generalise the essential features of discrete time GARCH processes, and are amenable to further analysis, possessing useful Markovian and stationarity properties.

• Dokumententyp: Paper
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch