Time-varying joint distribution through copulas

M. Concepcion Ausin, Hedibert F. Lopes

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

The analysis of temporal dependence in multivariate time series is considered. The dependence structure between the marginal series is modelled through the use of copulas which, unlike the correlation matrix, give a complete description of the joint distribution. The parameters of the copula function vary through time, following certain evolution equations depending on their previous values and the historical data. The marginal time series follow standard univariate GARCH models. Full Bayesian inference is developed where the whole set of model parameters is estimated simultaneously. This represents an essential difference from previous approaches in the literature where the marginal and the copula parameters are estimated separately in two consecutive steps. Moreover, a Bayesian procedure is proposed for the estimation of several measures of risk, such as the variance, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a portfolio of assets, providing point estimates and predictive intervals. The proposed copula model enables to capture the dependence structure between the individual assets which strongly influences these risk measures. Finally, the problem of optimal portfolio selection based on the estimation of meanvariance, meanVaR and meanCVaR efficient frontiers is also addressed. The proposed approach is illustrated with simulated and real financial time series.

Original languageEnglish (US)
Pages (from-to)2383-2399
Number of pages17
JournalComputational Statistics and Data Analysis
Volume54
Issue number11
DOIs
StatePublished - Nov 1 2010
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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