Family of multivariate distributions formed by mixing a mixture of generalized inverse Gaussian distributions: inference and applications to finance

There are well-known families of heavy-tailed multivariate distributions that include the normal distribution, as a member, that are built based on positive random variables as mixing distribution, where some members are special cases of generalized Inverse Gaussian (GIG) distributions. In this paper, we use a mixture of GIG distributions as mixing distribution to derive a new family of symmetric multivariate distributions. Resulting distributions produce a flexible family of symmetric distributions that are useful to fit observations quite concentrated around the median due to its leptokurtic property, which has applications in finance. For this specific purpose, we consider the Capital Asset Pricing Model (CAPM) under the proposed distribution. We derive some properties for the distribution and also developed an EM algorithm for computing the maximum likelihood (ML) estimates of the model parameters. Simulation studies demonstrate a good performance of the proposed algorithm, and the corresponding asymptotic properties of the estimates. Finally, we illustrate the obtained results with two real datasets from finance.