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Efficient Bayesian inference for stochastic time-varying copula models

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  • Almeida, Carlos
  • Czado, Claudia
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    Abstract

    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 naïve approach using Metropolis–Hastings 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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1511-1527

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1511-1527

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Time varying dependence; Non-Gaussian copulas; Kendall’s τ; Bayesian inference; Markov Chain Monte Carlo; Coarse grid sampler;

    References

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    Cited by:
    1. Stöber, Jakob & Czado, Claudia, 2014. "Regime switches in the dependence structure of multidimensional financial data," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 672-686.
    2. So, Mike K.P. & Yeung, Cherry Y.T., 2014. "Vine-copula GARCH model with dynamic conditional dependence," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 655-671.
    3. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.

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