Likelihood-free Bayesian inference for alpha-stable models

TL;DR

This paper introduces a likelihood-free Bayesian inference method for alpha-stable distributions, enabling analysis in higher dimensions where traditional densities are unavailable, demonstrated on currency data.

Contribution

It develops a novel likelihood-free Bayesian approach for multivariate alpha-stable models, overcoming the limitations of intractable densities.

Findings

Effective inference in 1, 2, and 3 dimensions

Application to real currency exchange rate data

Moderate computational cost

Abstract

$\alpha$-stable distributions are utilised as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate $\alpha$-stable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, $\alpha$-stable models are practically limited to the univariate setting under the Bayesian paradigm, and to bivariate models under the classical framework. In this article we develop a novel Bayesian approach to modelling univariate and multivariate $\alpha$-stable distributions based on recent advances in "likelihood-free" inference. We present an evaluation of the performance of this procedure in 1, 2 and 3 dimensions, and provide an analysis of real daily currency exchange rate data. The proposed approach provides a feasible inferential methodology at a moderate computational cost.