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Moments of MGOU processes and positive semidefinite matrix processes

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  • Behme, Anita

Abstract

Moment conditions for multivariate generalized Ornstein–Uhlenbeck (MGOU) processes are derived and the first and second moments are given in terms of the driving Lévy processes. In the second part of the paper a class of multivariate, positive semidefinite processes of MGOU-type is developed and suggested for use as squared volatility process in multivariate financial modeling.

Suggested Citation

  • Behme, Anita, 2012. "Moments of MGOU processes and positive semidefinite matrix processes," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 183-197.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:183-197
    DOI: 10.1016/j.jmva.2012.04.009
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    References listed on IDEAS

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    1. Behme, Anita & Lindner, Alexander, 2012. "Multivariate generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1487-1518.
    2. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
    3. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
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    Cited by:

    1. Anita Behme & Sebastian Mentemeier, 2025. "Limit Theorems for Stochastic Exponentials of Matrix-Valued Lévy Processes," Journal of Theoretical Probability, Springer, vol. 38(3), pages 1-40, September.
    2. Thiago do Rêgo Sousa & Robert Stelzer, 2022. "Moment‐based estimation for the multivariate COGARCH(1,1) process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 681-717, June.

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