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Maximum likelihood estimation for Wishart processes


  • Alfonsi, Aurélien
  • Kebaier, Ahmed
  • Rey, Clément


In the last decade, there has been a growing interest to use Wishart processes for modeling, especially for financial applications. However, there are still few studies on the estimation of its parameters. Here, we study the Maximum Likelihood Estimator (MLE) in order to estimate the drift parameters of a Wishart process. We obtain precise convergence rates and limits for this estimator in the ergodic case and in some nonergodic cases. We check that the MLE achieves the optimal convergence rate in each case. Motivated by this study, we also present new results on the Laplace transform that extend the recent findings of Gnoatto and Grasselli (2014) and are of independent interest.

Suggested Citation

  • Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
  • Handle: RePEc:eee:spapps:v:126:y:2016:i:11:p:3243-3282
    DOI: 10.1016/

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    References listed on IDEAS

    1. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137,, revised Apr 2011.
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    4. Da Fonseca José & Grasselli Martino & Ielpo Florian, 2014. "Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 1-37, May.
    5. Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 815-824, June.
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    7. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
    8. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Post-Print hal-00491371, HAL.
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