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Parametric estimation of a bivariate stable Lévy process

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  • Esmaeili, Habib
  • Klüppelberg, Claudia

Abstract

We propose a parametric model for a bivariate stable Lévy process based on a Lévy copula as a dependence model. We estimate the parameters of the full bivariate model by maximum likelihood estimation. As an observation scheme we assume that we observe all jumps larger than some [epsilon]>0 and base our statistical analysis on the resulting compound Poisson process. We derive the Fisher information matrix and prove asymptotic normality of all estimates when the truncation point [epsilon]-->0. A simulation study investigates the loss of efficiency because of the truncation.

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  • Esmaeili, Habib & Klüppelberg, Claudia, 2011. "Parametric estimation of a bivariate stable Lévy process," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 918-930, May.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:5:p:918-930
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    References listed on IDEAS

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    1. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    2. Ole E. Barndorff‐Nielsen & Alexander M. Lindner, 2007. "Lévy Copulas: Dynamics and Transforms of Upsilon Type," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 298-316, June.
    3. Esmaeili, Habib & Klüppelberg, Claudia, 2010. "Parameter estimation of a bivariate compound Poisson process," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 224-233, October.
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    1. Habib Esmaeili & Claudia Klüppelberg, 2013. "Two-Step Estimation Of A Multi-Variate Lévy Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 668-690, November.
    2. Grothe, Oliver & Nicklas, Stephan, 2013. "Vine constructions of Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 1-15.
    3. Beghin, Luisa & Macci, Claudio & Ricciuti, Costantino, 2020. "Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6364-6387.
    4. Riva-Palacio, Alan & Leisen, Fabrizio, 2021. "Compound vectors of subordinators and their associated positive Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

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