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.

中文翻译：

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多元回火稳定分布的估计与模拟

我们介绍了一种用于多变量回火稳定分布的模拟和参数估计的方法，重点是双变量情况。由于频谱测量的离散化，我们的方法基于近似值。然后将其应用于与汇率相关的两个双变量金融数据集。第一个是标准货币之间的汇率，第二个是基于与加密货币相关的汇率。我们的近似结果适用于广泛的多元无限可分分布。