Likelihood-Free Bayesian Inference for α-Stable Models

33 Pages Posted: 10 Jun 2017

See all articles by Gareth Peters

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics

Y. Fan

University of New South Wales (UNSW) - School of Mathematics and Statistics

Date Written: December 23, 2009

Abstract

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

Keywords: α-stable distributions; Approximate Bayesian computation; Bayesian inference; Likelihood-free inference; Multivariate models

Suggested Citation

Peters, Gareth and Sisson, Scott and Fan, Y., Likelihood-Free Bayesian Inference for α-Stable Models (December 23, 2009). Available at SSRN: https://ssrn.com/abstract=2980440 or http://dx.doi.org/10.2139/ssrn.2980440

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

Y. Fan

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

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