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Time-varying joint distribution through copulas

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  • Ausin, M. Concepcion
  • Lopes, Hedibert F.

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 mean-variance, mean-VaR and mean-CVaR efficient frontiers is also addressed. The proposed approach is illustrated with simulated and real financial time series.

Suggested Citation

  • Ausin, M. Concepcion & Lopes, Hedibert F., 2010. "Time-varying joint distribution through copulas," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2383-2399, November.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2383-2399
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    Cited by:

    1. Xiaochun Liu, 2016. "Markov switching quantile autoregression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 356-395, November.
    2. Janus, Paweł & Koopman, Siem Jan & Lucas, André, 2014. "Long memory dynamics for multivariate dependence under heavy tails," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 187-206.
    3. Galeano San Miguel, Pedro & Ausín Olivera, María Concepción & Nguyen, Hoang, 2017. "Parallel Bayesian Inference for High Dimensional Dynamic Factor Copulas," DES - Working Papers. Statistics and Econometrics. WS 24552, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    5. Carta, Alessandro & Steel, Mark F.J., 2012. "Modelling multi-output stochastic frontiers using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3757-3773.
    6. 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.
    7. Atil, Ahmed & Bradford, Marc & Elmarzougui, Abdelaziz & Lahiani, Amine, 2016. "Conditional dependence of US and EU sovereign CDS: A time-varying copula-based estimation," Finance Research Letters, Elsevier, vol. 19(C), pages 42-53.
    8. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    9. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    10. Arthur Charpentier, 2015. "Prévision avec des copules en finance," Working Papers hal-01151233, HAL.
    11. Alp, Tansel & Demetrescu, Matei, 2010. "Joint forecasts of Dow Jones stocks under general multivariate loss function," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2360-2371, November.
    12. Domínguez, M. C. & Gómez, M. & Ausín, Concepción, 2015. "Seasonal copula models for the analysis of glacier discharge at King George Island, Antarctica," DES - Working Papers. Statistics and Econometrics. WS ws1513, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Hela Mzoughi & Faysal Mansouri, 2013. "Computing risk measures for non-normal asset returns using Copula theory," The Empirical Econometrics and Quantitative Economics Letters, Faculty of Economics, Chiang Mai University, vol. 2(1), pages 59-70, March.
    14. 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.
    15. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2012. "Global Risk Evolution and Diversification: a Copula-DCC-GARCH Model Approach," Brazilian Review of Finance, Brazilian Society of Finance, vol. 10(4), pages 529-550.
    16. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    17. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    18. 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.

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