Efficient Bayesian inference for stochastic time-varying copula models

Carlos Almeida, Claudia Czado

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


There is strong empirical evidence that dependence in multivariate financial time series varies over time. To model this effect, a time varying copula class is developed, which is called the stochastic copula autoregressive (SCAR) model. Dependence at time t is modeled by a real-valued latent variable, which corresponds to the Fisher Z transformation of Kendall's τ for the chosen copula family. This allows for a common scale so that a general range of copula families including the Gaussian, Clayton and Gumbel copulas can be used and compared in our modeling framework. The inclusion of latent variables makes maximum likelihood estimation computationally difficult, therefore a Bayesian approach is followed. This approach allows the computation of credibility intervals in addition to point estimates. Two Markov Chain Monte Carlo (MCMC) sampling algorithms are proposed. The first one is a nave approach using MetropolisHastings within Gibbs, while the second is a more efficient coarse grid sampler. The performance of these samplers are investigated in a simulation study and are applied to data involving financial stock indices. It is shown that time varying dependence is present for this data and can be quantified by estimating the underlying time varying Kendall's τ with point-wise credible intervals.

Original languageEnglish
Pages (from-to)1511-1527
Number of pages17
JournalComputational Statistics and Data Analysis
Issue number6
StatePublished - Jun 2012


  • Bayesian inference
  • Coarse grid sampler
  • Kendall's τ
  • Markov Chain Monte Carlo
  • Non-Gaussian copulas
  • Time varying dependence


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