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Copula based models for serial dependence

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  • Beatriz Vaz de Melo Mendes
  • Cecília Aíube
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    Abstract

    Purpose – This paper aims to statistically model the serial dependence in the first and second moments of a univariate time series using copulas, bridging the gap between theory and applications, which are the focus of risk managers. Design/methodology/approach – The appealing feature of the method is that it captures not just the linear form of dependence (a job usually accomplished by ARIMA linear models), but also the non-linear ones, including tail dependence, the dependence occurring only among extreme values. In addition it investigates the changes in the mean modeling after whitening the data through the application of GARCH type filters. A total 62 US stocks are selected to illustrate the methodologies. Findings – The copula based results corroborate empirical evidences on the existence of linear and non-linear dependence at the mean and at the volatility levels, and contributes to practice by providing yet a simple but powerful method for capturing the dynamics in a time series. Applications may follow and include VaR calculation, simulations based derivatives pricing, and asset allocation decisions. The authors recall that the literature is still inconclusive as to the most appropriate value-at-risk computing approach, which seems to be a data dependent decision. Originality/value – This paper uses a conditional copula approach for modeling the time dependence in the mean and variance of a univariate time series.

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    Bibliographic Info

    Article provided by Emerald Group Publishing in its journal International Journal of Managerial Finance.

    Volume (Year): 7 (2011)
    Issue (Month): 1 (February)
    Pages: 68-82

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    Handle: RePEc:eme:ijmfpp:v:7:y:2011:i:1:p:68-82

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    Related research

    Keywords: Financial analysis; Multivariate analysis; Time series analysis; United States of America;

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    References

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    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    2. Beare, Brendan K., 2010. "Archimedean Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt0xh8q1g3, Department of Economics, UC San Diego.
    3. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
    4. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
    5. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    6. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    7. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    8. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    10. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    11. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, 01.
    12. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    13. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
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