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Research Article

Estimation and simulation for multivariate tempered stable distributions

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Pages 451-475 | Received 04 Dec 2020, Accepted 28 Jul 2021, Published online: 01 Sep 2021
 

Abstract

We introduce a methodology for the simulation and parameter estimation of multivariate tempered stable distributions with an emphasis on the bivariate case. Our approach is based on an approximation due to a discretization of the spectral measure. It is then applied to two bivariate financial datasets related to exchange rates. The first is comprised of exchange rates between standard currencies, while the second is based on exchange rates related to cryptocurrencies. Our approximation results hold for a wide class of multivariate infinitely divisible distributions.

2010 Mathematics Subject Classifications:

Acknowledgments

The authors would like to thank the three anonymous referees whose comments lead to improvement in the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Russian Science Foundation [17-11-01098].

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