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Conditional Dependency of Financial Series: An Application of Copulas


  • Rockinger, M.
  • Jondeau, E.


We develop a new methodology that measures conditional dependency. We achieve this by using copula functions that link marginal distributions, here chosen to obey a GARCH-type model with time-varying skewness and kurtosis. We apply this model to daily returns of stock-market indices. We find strong evidence of persistence in dependency both for local currency and $ US denominated series. For European stock markets, we also find evidence that large simultaneous returns of either sign lead to higher subsequent dependency. We show that dependency changes through time, as well. For stock markets within Europe, dependency increased whereas it decreased since the mid 90s when involving the S&P 500 or the Nikkei. We also suggest extensions for conditional asset pricing models involving time variation of co-skewness and co-kurtosis.

Suggested Citation

  • Rockinger, M. & Jondeau, E., 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working papers 82, Banque de France.
  • Handle: RePEc:bfr:banfra:82

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    References listed on IDEAS

    1. Ratner, Mitchell, 1992. "Portfolio diversification and the inter-temporal stability of international stock indices," Global Finance Journal, Elsevier, vol. 3(1), pages 67-77.
    2. 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 705-730, August.
    3. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    4. Bekaert, Geert & Harvey, Campbell R, 1995. " Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
    5. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
    6. Roberto Rigobon, 1999. "On the Measurement of the International Propagation of Shocks," NBER Working Papers 7354, National Bureau of Economic Research, Inc.
    7. Rockinger, Michael & Urga, Giovanni, 2001. "A Time-Varying Parameter Model to Test for Predictability and Integration in the Stock Markets of Transition Economies," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 73-84, January.
    8. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    9. Andrew Ang & Geert Bekaert, 1999. "International Asset Allocation with Time-Varying Correlations," NBER Working Papers 7056, National Bureau of Economic Research, Inc.
    10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    11. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    12. Ramchand, Latha & Susmel, Raul, 1998. "Volatility and cross correlation across major stock markets," Journal of Empirical Finance, Elsevier, vol. 5(4), pages 397-416, October.
    13. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    14. Terry A. Marsh & Niklas Wagner, 2004. "Return-Volume Dependence and Extremes in International Equity Markets," Finance 0401007, EconWPA.
    15. Brian H. Boyer & Michael S. Gibson & Mico Loretan, 1997. "Pitfalls in tests for changes in correlations," International Finance Discussion Papers 597, Board of Governors of the Federal Reserve System (U.S.).
    16. Tse, Y. K., 2000. "A test for constant correlations in a multivariate GARCH model," Journal of Econometrics, Elsevier, vol. 98(1), pages 107-127, September.
    17. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    18. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    19. Susmel, Raul & Engle, Robert F., 1994. "Hourly volatility spillovers between international equity markets," Journal of International Money and Finance, Elsevier, vol. 13(1), pages 3-25, February.
    20. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
    21. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    22. Michael Rockinger & Eric Jondeau, 2000. "Entropy Densities," Working Papers hal-00601485, HAL.
    23. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    24. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    25. Barone-Adesi, Giovanni, 1985. "Arbitrage Equilibrium with Skewed Asset Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(03), pages 299-313, September.
    26. Karolyi, G Andrew, 1995. "A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility: The Case of the United States and Canada," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 11-25, January.
    27. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
    28. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    29. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    30. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
    31. Jondeau, E. & Rockinger, M., 2000. "Conditional Volatility, Skewness, and Kurtosis: Existence and Persistence," Working papers 77, Banque de France.
    32. Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
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    Cited by:

    1. Morana, Claudio & Beltratti, Andrea, 2008. "Comovements in international stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(1), pages 31-45, February.
    2. Chen, Kuan-Ju & Chen, Kuan-Heng, 2016. "Analysis of Energy and Agricultural Commodity Markets with the Policy Mandated: A Vine Copula-based ARMA-EGARCH Model," 2016 Annual Meeting, July 31-August 2, 2016, Boston, Massachusetts 236028, Agricultural and Applied Economics Association.
    3. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 399-421.
    4. Aamir R. Hashmi & Anthony S. Tay, 2001. "Global and Regional Sources of Risk in Equity Markets: Evidence from Factor Models with Time-Varying Conditional Skewness," Departmental Working Papers wp0116, National University of Singapore, Department of Economics.
    5. Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA.
    6. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies.
    7. Pedro Alberto Morettin & Clélia Maria de Castro Toloi & Chang Chiann & José Carlos Simon de Miranda, 2010. "Wavelet Smoothed Empirical Copula Estimators," Brazilian Review of Finance, Brazilian Society of Finance, vol. 8(3), pages 263-281.
    8. Claudio Morana, 2008. "International stock markets comovements: the role of economic and financial integration," Empirical Economics, Springer, vol. 35(2), pages 333-359, September.
    9. Ane, Thierry & Labidi, Chiraz, 2006. "Spillover effects and conditional dependence," International Review of Economics & Finance, Elsevier, vol. 15(4), pages 417-442.
    10. repec:bla:ausecp:v:56:y:2017:i:2:p:134-162 is not listed on IDEAS
    11. repec:eee:ecmode:v:64:y:2017:i:c:p:409-418 is not listed on IDEAS
    12. Junker, Markus & Szimayer, Alex & Wagner, Niklas, 2006. "Nonlinear term structure dependence: Copula functions, empirics, and risk implications," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1171-1199, April.
    13. Söehnke Bartram & Stephen Taylor & Yaw-Huei Wang, 2004. "The Euro and European Financial Market Integration," Money Macro and Finance (MMF) Research Group Conference 2004 49, Money Macro and Finance Research Group, revised 13 Oct 2004.
    14. Beatriz Vaz de Melo Mendes, 2005. "Computing Conditional VaR using Time-varying CopulasComputing Conditional VaR using Time-varying Copulas," Brazilian Review of Finance, Brazilian Society of Finance, vol. 3(2), pages 251-265.
    15. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    16. repec:wsi:ijtafx:v:13:y:2010:i:02:n:s0219024910005759 is not listed on IDEAS
    17. Koirala, Krishna H. & Mishra, Ashok K. & D'Antoni, Jeremy M. & Mehlhorn, Joey E., 2015. "Energy prices and agricultural commodity prices: Testing correlation using copulas method," Energy, Elsevier, vol. 81(C), pages 430-436.
    18. Hashmi, Aamir R. & Tay, Anthony S., 2007. "Global regional sources of risk in equity markets: Evidence from factor models with time-varying conditional skewness," Journal of International Money and Finance, Elsevier, vol. 26(3), pages 430-453, April.
    19. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    20. Eduardo F. L. de Melo & Beatriz Vaz de Melo Mendes, 2009. "Local Estimation of Copula Based Value-at-Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 7(1), pages 29-50.
    21. Patton, Andrew J, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series qt3fc1c8hw, Department of Economics, UC San Diego.
    22. Yanqin Fan & Xiaohong Chen, 2004. "Estimation of Copula-Based Semiparametric Time Series Models," Econometric Society 2004 Far Eastern Meetings 559, Econometric Society.

    More about this item


    International correlation ; Market integration ; ARCH; Stock indices.;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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