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February 2010 Multivariate COGARCH(1, 1) processes
Robert Stelzer
Bernoulli 16(1): 80-115 (February 2010). DOI: 10.3150/09-BEJ196

Abstract

Multivariate COGARCH(1, 1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent time-varying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices.

After defining the COGARCH(1, 1) process, we analyze its probabilistic properties. We show a sufficient condition for the existence of a stationary distribution for the stochastic covariance matrix process and present criteria ensuring the finiteness of moments. Under certain natural assumptions on the moments of the driving Lévy process, explicit expressions for the first and second-order moments and (asymptotic) second-order stationarity of the covariance matrix process are obtained. Furthermore, we study the stationarity and second-order structure of the increments of the multivariate COGARCH(1, 1) process and their “squares”.

Citation

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Robert Stelzer. "Multivariate COGARCH(1, 1) processes." Bernoulli 16 (1) 80 - 115, February 2010. https://doi.org/10.3150/09-BEJ196

Information

Published: February 2010
First available in Project Euclid: 12 February 2010

zbMATH: 1200.62110
MathSciNet: MR2648751
Digital Object Identifier: 10.3150/09-BEJ196

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

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Vol.16 • No. 1 • February 2010
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