Electronic Journal of Statistics

Bayesian inference for the extremal dependence

Giulia Marcon, Simone A. Padoan, and Isadora Antoniano-Villalobos

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Abstract

A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach nonparametric. Although the analytical expression of the posterior is unknown, inference is possible via a trans-dimensional MCMC scheme. We show the efficiency of the proposed methodology by means of a simulation study. The extremal behaviour of log-returns of daily exchange rates between the Pound Sterling vs the U.S. Dollar and the Pound Sterling vs the Japanese Yen is analysed for illustrative purposes.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 3310-3337.

Dates
Received: December 2015
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1479287223

Digital Object Identifier
doi:10.1214/16-EJS1162

Mathematical Reviews number (MathSciNet)
MR3572851

Zentralblatt MATH identifier
1357.62213

Subjects
Primary: 62G05: Estimation 62G07: Density estimation 62G32: Statistics of extreme values; tail inference

Keywords
Generalised extreme value distribution extremal dependence angular measure max-stable distribution Bernstein polynomials Bayesian nonparametrics trans-dimensional MCMC exchange rates

Citation

Marcon, Giulia; Padoan, Simone A.; Antoniano-Villalobos, Isadora. Bayesian inference for the extremal dependence. Electron. J. Statist. 10 (2016), no. 2, 3310--3337. doi:10.1214/16-EJS1162. https://projecteuclid.org/euclid.ejs/1479287223


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