Copulas and Dependency Measures for Multivariate Linnik Distributions

We begin this paper by introducing the Linnik distributions in both the univariate and multivariate case. An overview of simulation methods and two estimation procedures for the multivariate Linnik distribution are presented. Experiments demonstrating the accuracy of the procedures are also included. Then a novel multivariate Linnik copula is derived. The primary focus of this part of work is on simulation and estimation procedures for this copula, applying existing algorithms for simulation and estimation procedures for the multivariate Linnik distribution derived in the prior section. Several theoretical properties of the copula in relation to different dependence metrics are derived.

Linnik distributions and processes

Using a simple characterization of the Linnik distribution, discrete-time processes having a stationary Linnik distribution are constructed. The processes are structurally related to exponential processes introduced by Arnold (1989), Lawrance and Lewis (1981) and Gaver and Lewis (1980). Multivariate versions of the processes are also described. These Linnik models appear to be viable alternatives to stable processes as models for temporal changes in stock prices.