Bayesian skew selection for multivariate models

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio, 2003 A. Azzalini and A. Capitanio, Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society. Series B, 65 (2003), pp. 367a??389. View Record in Scopus Full Text via CrossRef Cited By in Scopus (166)Azzalini and Capitanio (2003) or Sahu et al. (2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, the prior smoothly bounds the non-zero skew parameters away from zero and identifies the posterior. We estimate the model using Markov chain Monte Carlo (MCMC) methods by exploiting the conditionally Gaussian representation of the skew t distributions. This allows for the search through the posterior space of all possible combinations of skew and symmetry in each dimension. We show that the proposed method works well in a simulation setting, and employ it in two multivariate econometric examples. The first involves the modeling of foreign exchange rates and the second is a vector autoregression for intra-day electricity spot prices. The approach selects skew along the original coordinates of the data, which proves insightful in both examples.
Original languageEnglish
Pages (from-to)1824 - 1839
Number of pages16
JournalComputational Statistics and Data Analysis
Volume54
Issue number7
Publication statusPublished - 2010
Externally publishedYes

Cite this

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title = "Bayesian skew selection for multivariate models",
abstract = "We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio, 2003 A. Azzalini and A. Capitanio, Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society. Series B, 65 (2003), pp. 367a??389. View Record in Scopus Full Text via CrossRef Cited By in Scopus (166)Azzalini and Capitanio (2003) or Sahu et al. (2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, the prior smoothly bounds the non-zero skew parameters away from zero and identifies the posterior. We estimate the model using Markov chain Monte Carlo (MCMC) methods by exploiting the conditionally Gaussian representation of the skew t distributions. This allows for the search through the posterior space of all possible combinations of skew and symmetry in each dimension. We show that the proposed method works well in a simulation setting, and employ it in two multivariate econometric examples. The first involves the modeling of foreign exchange rates and the second is a vector autoregression for intra-day electricity spot prices. The approach selects skew along the original coordinates of the data, which proves insightful in both examples.",
author = "Anastasios Panagiotelis and Michael Smith",
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journal = "Computational Statistics and Data Analysis",
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Bayesian skew selection for multivariate models. / Panagiotelis, Anastasios; Smith, Michael.

In: Computational Statistics and Data Analysis, Vol. 54, No. 7, 2010, p. 1824 - 1839.

Research output: Contribution to journalArticleResearchpeer-review

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AB - We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio, 2003 A. Azzalini and A. Capitanio, Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society. Series B, 65 (2003), pp. 367a??389. View Record in Scopus Full Text via CrossRef Cited By in Scopus (166)Azzalini and Capitanio (2003) or Sahu et al. (2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether there is symmetry, or skew, in each dimension. We adopt a proper beta prior on each non-zero skew coefficient, and derive the corresponding prior on the skew parameters. In both distributions we show that as the degrees of freedom increases, the prior smoothly bounds the non-zero skew parameters away from zero and identifies the posterior. We estimate the model using Markov chain Monte Carlo (MCMC) methods by exploiting the conditionally Gaussian representation of the skew t distributions. This allows for the search through the posterior space of all possible combinations of skew and symmetry in each dimension. We show that the proposed method works well in a simulation setting, and employ it in two multivariate econometric examples. The first involves the modeling of foreign exchange rates and the second is a vector autoregression for intra-day electricity spot prices. The approach selects skew along the original coordinates of the data, which proves insightful in both examples.

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