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Efficient Bayesian inference for stochastic time-varying copula models

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  • Almeida, Carlos
  • Czado, Claudia

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.

Suggested Citation

  • Almeida, Carlos & Czado, Claudia, 2012. "Efficient Bayesian inference for stochastic time-varying copula models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1511-1527.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1511-1527
    DOI: 10.1016/j.csda.2011.08.015
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Bartels, Mariana & Ziegelmann, Flavio A., 2016. "Market risk forecasting for high dimensional portfolios via factor copulas with GAS dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 66-79.
    2. 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.
    3. Frazier, David T. & Liu, Xiaochun, 2016. "A new approach to risk-return trade-off dynamics via decomposition," Journal of Economic Dynamics and Control, Elsevier, vol. 62(C), pages 43-55.
    4. Małgorzata Doman & Ryszard Doman, 2014. "Dynamic Linkages in the Pairs (GBP/EUR, USD/EUR) and (GBP/USD, EUR/USD): How Do They Change During a Day?," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 6(1), pages 33-56, March.
    5. Jacek Osiewalski & Krzysztof Osiewalski, 2016. "Hybrid MSV-MGARCH Models – General Remarks and the GMSF-SBEKK Specification," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 8(4), pages 241-271, December.
    6. 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.
    7. Rub'en Loaiza-Maya & Michael S. Smith & Worapree Maneesoonthorn, 2017. "Time Series Copulas for Heteroskedastic Data," Papers 1701.07152, arXiv.org.
    8. repec:eee:jbfina:v:82:y:2017:i:c:p:1-19 is not listed on IDEAS
    9. Brechmann Eike Christain & Czado Claudia, 2013. "Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 307-342, December.
    10. repec:eee:quaeco:v:66:y:2017:i:c:p:275-293 is not listed on IDEAS
    11. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    12. 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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