Estimation of the parameters of multivariate stable distributions

Abstract

In this paper, we first discuss some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid method is proposed for the estimation of the parameters of a univariate stable distribution. The proposed method is further used for the estimation of the parameters of a strictly multivariate stable distribution. The efficiency, accuracy and simplicity of the new method is shown through Monte-Carlo simulation. Finally, we apply the proposed method to the univariate and bivariate financial data.

KEYWORDS:

• Multivariate stable distribution
• Parameter estimation
• Simulation
• Applications

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary
• 62F10
• Secondary
• 60E07

Acknowledgments

The authors would like to thank an anonymous reviewer for his/her valuable comments and suggestions to improve the manuscript. We are also thankful to Professor John P. Nolan for providing access to STABLE package designed for R which improved the computations and results.