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Dynamic D-Vine Copula Model with Applications to Value-at-Risk (VaR)

Author

Listed:
  • Tófoli Paula V.

    (Graduate Program in Economics, Catholic University of Brasilia, SGAN 916, Module B, Office A-120, Asa Norte, Brasilia, DF 70790-160, Brazil)

  • Ziegelmann Flávio A.

    (Department of Statistics, Federal University of Rio Grande do Sul, Porto Alegre, RS, Brazil)

  • Candido Osvaldo

    (Graduate Program in Economics, Catholic University of Brasilia, Brasilia, DF, Brazil)

  • Valls Pereira Pedro L.

    (Graduate Program in Economics, Sao Paulo School of Economics, Sao Paulo, SP, Brazil)

Abstract

Vine copulas are multivariate dependence models constructed from pair-copulas (bivariate copulas). In this paper, we allow the dependence parameters of the pair-copulas in a D-vine decomposition to be potentially time-varying, following a restricted ARMA(1, m) process, in order to obtain a very flexible dependence model for applications to multivariate financial return data. We investigate the dependence among the broad stock market indexes from Germany (DAX), France (CAC 40), Britain (FTSE 100), the United States (S&P 500) and Brazil (IBOVESPA) both in a crisis and in a non-crisis period. We find evidence of stronger dependence among the indexes in bear markets. Surprisingly, though, the dynamic D-vine copula indicates the occurrence of a sharp decrease in dependence between the indexes FTSE and CAC in the beginning of 2011, and also between CAC and DAX during mid-2011 and in the beginning of 2008, suggesting the absence of contagion in these cases. We evaluate the dynamic D-vine copula with respect to Value-at-Risk (VaR) forecasting accuracy in crisis periods. The dynamic D-vine outperforms the static D-vine in terms of predictive accuracy for our real data sets. We also investigate the dynamic D-vine copula in a simulation study and the overall results of the Monte Carlo experiments are quite favorable to the dynamic D-vine copula in comparison with a static D-vine copula.

Suggested Citation

  • Tófoli Paula V. & Ziegelmann Flávio A. & Candido Osvaldo & Valls Pereira Pedro L., 2019. "Dynamic D-Vine Copula Model with Applications to Value-at-Risk (VaR)," Journal of Time Series Econometrics, De Gruyter, vol. 11(2), pages 1-34, July.
    • Handle: RePEc:bpj:jtsmet:v:11:y:2019:i:2:p:34:n:2
    DOI: 10.1515/jtse-2017-0016
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    More about this item

    Keywords

    regular vine; pair-copula constructions; time-varying copulas; value-at-risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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