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Tracking a changing copula

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  • Harvey, Andrew

Abstract

A copula models the relationships between variables independently of their marginal distributions. When the variables are time series, the copula may change over time. Recursive procedures based on indicator variables are proposed for tracking these changes over time. Estimation of the unknown parameters is by maximum likelihood. When the marginal distributions change, pre-filtering is necessary before constructing the indicator variables on which the recursions are based. This entails estimating time-varying quantiles and a simple method based on time-varying histograms is proposed. The techniques are applied to the Hong Kong and Korean stock market indices. Some interesting and unexpected movements are detected, particularly after the attack on the Hong Kong dollar in 1997.

Suggested Citation

  • Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.
    • Handle: RePEc:eee:empfin:v:17:y:2010:i:3:p:485-500
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    References listed on IDEAS

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    1. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    3. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    4. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
    5. Kee-Hong Bae & G. Andrew Karolyi & René M. Stulz, 2003. "A New Approach to Measuring Financial Contagion," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 717-763, July.
    6. Fermanian, Jean-David & Scaillet, Olivier, 2003. "Nonparametric estimation of copulas for time series," Working Papers unige:41797, University of Geneva, Geneva School of Economics and Management.
    7. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
    8. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    9. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
    10. Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 106-131, Winter.
    11. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    12. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    13. Mardi Dungey & Renee Fry & Brenda Gonzalez-Hermosillo & Vance Martin, 2005. "Empirical modelling of contagion: a review of methodologies," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 9-24.
    14. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    15. 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, May.
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    Cited by:

    1. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, October.
    2. Mensi, Walid & Selmi, Refk & Al-Yahyaee, Khamis Hamed, 2020. "Switching dependence and systemic risk between crude oil and U.S. Islamic and conventional equity markets: A new evidence," Resources Policy, Elsevier, vol. 69(C).
    3. Harvey, Andrew & Thiele, Stephen, 2016. "Testing against changing correlation," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 575-589.
    4. Selmi, Refk & Hammoudeh, Shawkat & Kasmaoui, Kamal & Sousa, Ricardo M. & Errami, Youssef, 2022. "The dual shocks of the COVID-19 and the oil price collapse: A spark or a setback for the circular economy?," Energy Economics, Elsevier, vol. 109(C).
    5. Camirand Lemyre, Felix & Decrouez, Geoffrey, 2021. "Nonparametric recursive estimation of the copula," Statistics & Probability Letters, Elsevier, vol. 168(C).
    6. Harvey, Andrew & Oryshchenko, Vitaliy, 2012. "Kernel density estimation for time series data," International Journal of Forecasting, Elsevier, vol. 28(1), pages 3-14.
    7. Wang, Yi-Chiuan & Wu, Jyh-Lin & Lai, Yi-Hao, 2013. "A revisit to the dependence structure between the stock and foreign exchange markets: A dependence-switching copula approach," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1706-1719.
    8. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    9. Fry-McKibbin, Renée & Martin, Vance L. & Tang, Chrismin, 2014. "Financial contagion and asset pricing," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 296-308.
    10. Selmi, Refk & Wohar, Mark & Deisting, Florent & Kasmaoui, Kamal, 2023. "Dynamic inflation hedging performance and downside risk: A comparison between Islamic and conventional stock indices," The Quarterly Review of Economics and Finance, Elsevier, vol. 91(C), pages 56-67.
    11. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    12. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    13. Semeyutin, Artur & O’Neill, Robert, 2019. "A brief survey on the choice of parameters for: “Kernel density estimation for time series data”," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).

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