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Handbook of Financial Time Series pp 767–785Cite as

Copula–Based Models for Financial Time Series

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Abstract

This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to characterize the (conditional) cross-sectional dependence between individual time series, and in univariate time series analysis, where they are used to characterize the dependence between a sequence of observations of a scalar time series process. The paper includes a broad, brief, review of the many applications of copulas in finance and economics.

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References

  • Alexander, C. 2008: Market Risk Analysis, Volume III. Wiley & Sons, London, forthcoming.

    Google Scholar 

  • Alexander, C. and Chibumba, A. (1997): Multivariate Orthogonal Factor GARCH. Mimeo, University of Sussex.

    Google Scholar 

  • Alsina, C., Nelsen, R.B. and Schweizer, B. (1993): On the characterization of a class of binary operations on distribution functions. Statistics and Probability Letters 17, 85–89.

    Article  MATH  MathSciNet  Google Scholar 

  • Andersen, T.G., Bollerslev, T., Christoffersen, P.F. and Diebold, F.X. (2006): Volatility and Correlation Forecasting. In: Elliott, G., Granger, C.W.J. and Timmermann, A. (Eds.): The Handbook of Economic Forecasting. North Holland, Amsterdam.

    Google Scholar 

  • Ang, A. and Bekaert, G. (2002): International Asset Allocation with Regime Shifts. Review of Financial Studies 15, 1137–1187.

    Article  Google Scholar 

  • Ang, A. and Chen, J. (2002): Asymmetric Correlations of Equity Portfolios. Journal of Financial Economics 63, 443–494.

    Article  Google Scholar 

  • Arakelian, V. and Dellaportas, P. (2005): Contagion tests via copula threshold models. Mimeo, University of Crete.

    Google Scholar 

  • Bartram, S.M., Taylor, S.J. and Wang, Y.-H. (2006): The euro and European financial market dependence. Journal of Banking and Finance forthcoming.

    Google Scholar 

  • Bae, K.-H., Karolyi, G.A. and Stulz, R.M. (2003): A New Approach to Measuring Financial Contagion. Review of Financial Studies 16, 717–764.

    Article  Google Scholar 

  • Bauwens, L., Laurent, S. and Rombouts, J. (2006): Multivariate GARCH Models: A Survey. Journal of Applied Econometrics 21, 79–109.

    Article  MathSciNet  Google Scholar 

  • Beare, B. (2007): Copula-based mixing conditions for Markov chains. Mimeo, University of Oxford.

    Google Scholar 

  • Bennett, M.N. and Kennedy, J.E. (2004): Quanto Pricing with Copulas. Journal of Derivatives 12, 26–45.

    Google Scholar 

  • Bollerslev, T. (1986): Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31, 307–327.

    Article  MATH  MathSciNet  Google Scholar 

  • Bonhomme, S. and Robin, J.-M. (2004): Modeling Individual Earnings Trajectories using Copulas with an Application to the Study of Earnings Inequality: France, 1990–2002. Mimeo, Université de Paris 1.

    Google Scholar 

  • Bouyé, E. and Salmon, M. (2002): Dynamic Copula Quantile Regressions and Tail Area Dynamic Dependence in Forex Markets. Mimeo, University of Warwick.

    Google Scholar 

  • Brendstrup, B. and Paarsch, H.J. (2007): Semiparametric Identification and Estimation in Multi-Object English Auctions. Journal of Econometrics 141, 84–108.

    Article  MathSciNet  Google Scholar 

  • Breymann, W., Dias, A. and Embrechts, P. (2003): Dependence structures for multivariate high-frequency data in finance. Quantitative Finance 3, 1–16.

    Article  MathSciNet  Google Scholar 

  • Capéraà, P., Fougères, A.-L. and Genest, C. (1997): A Nonparametric Estimation Procedure for Bivariate Extreme Value Copulas. Biometrika 84, 567–577.

    Article  MATH  MathSciNet  Google Scholar 

  • Cappiello, L., Engle, R.F. and Sheppard, K. (2003): Evidence of Asymmetric Effects in the Dynamics of International Equity and Bond Return Covariance. Journal of Financial Econometrics forthcoming.

    Google Scholar 

  • Carrasco M. and Chen X. (2002): Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17–39.

    Article  MATH  MathSciNet  Google Scholar 

  • Casella, G. and Berger, R.L. (1990): Statistical Inference Duxbury Press, U.S.A.

    MATH  Google Scholar 

  • Chamberlain, G. (1983): A characterization of the distributions that imply mean-variance utility functions. Journal of Economic Theory 29, 185–201.

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, X. and Fan, Y. (2006a): Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307–335.

    Article  MathSciNet  Google Scholar 

  • Chen, X. and Fan, Y. (2006b): Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135, 125–154.

    Article  MathSciNet  Google Scholar 

  • Chen, X., Fan, Y. and Tsyrennikov, V. (2006): Efficient estimation of semiparametric multivariate copula models. Journal of the American Statistical Association 101, 1228–1240.

    Article  MATH  MathSciNet  Google Scholar 

  • Cherubini, U. and Luciano, E. (2001): Value at Risk trade-off and capital allocation with copulas. Economic Notes 30, 235–256.

    Article  Google Scholar 

  • Cherubini, U., Luciano, E. and Vecchiato, W. (2004): Copula Methods in Finance John Wiley & Sons, England.

    MATH  Google Scholar 

  • Chollete, L. (2005): Frequent extreme events? A dynamic copula approach. Mimeo, Norwegian School of Economics and Business.

    Google Scholar 

  • Chollete, L., de la Peña, V. and Lu, C.-C. (2005): Comovement of international financial markets. Mimeo, Norwegian School of Economics and Business.

    Google Scholar 

  • Christoffersen, P. (2008): Value–at–Risk models. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T. (Eds.): Handbook of Financial Time Series, 752–766. Springer Verlag, New York.

    Google Scholar 

  • Clayton, D.G. (1978): A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 141–151.

    Article  MATH  MathSciNet  Google Scholar 

  • Coles, S., Heffernan, J. and Tawn, J. (1999): Dependence measures for extreme value analyses. Extremes 2, 339–365.

    Article  MATH  Google Scholar 

  • Cook, R.D. and Johnson, M.E. (1981): A family of distributions for modelling non-elliptically symmetric multivariate data. Journal of the Royal Statistical Society 43, 210–218.

    MATH  MathSciNet  Google Scholar 

  • Corradi V. and Swanson, N.R. (2005): Predictive Density Evaluation. In: Elliott, G., Granger, C.W.J. and Timmermann, A. (Eds.): Handbook of Economic Forecasting. North Holland, Amsterdam.

    Google Scholar 

  • Darsow, W.F., Nguyen, B. and Olsen, E.T. (1992): Copulas and Markov processes. Illinois Journal of Mathematics 36, 600–642.

    MATH  MathSciNet  Google Scholar 

  • Daul, S., De Giorgi, E., Lindskog, F. and McNeil, A. (2003): The grouped t-copula with an application to credit risk. RISK 16, 73–76.

    Google Scholar 

  • Demarta, S. and McNeil, A.J. (2005): The t copula and related copulas. International Statistical Review 73, 111–129.

    MATH  Google Scholar 

  • Denuit, M. and Lambert, P. (2005): Constraints on concordance measures in bivariate discrete data. Journal of Multivariate Analysis 93, 40–57.

    Article  MATH  MathSciNet  Google Scholar 

  • Diebold, F.X., Gunther, T. and Tay, A.S. (1998): Evaluating Density Forecasts with Applications to Financial Risk Management. International Economic Review 39, 863–883.

    Article  Google Scholar 

  • Diebold, F.X., Hahn, J. and Tay, A.S. (1999): Multivariate Density Forecast Evaluation and Calibration in Financial Risk Management: High Frequency Returns on Foreign Exchange. Review of Economics and Statistics 81, 661–673.

    Article  Google Scholar 

  • Duffie, D. (2004): Clarendon Lecture in Finance, mimeo Stanford University. http://www.finance.ox.ac.uk/NR/rdonlyres/9A26FC79-980F-4114-8033-B73899EADE88/0/slides_duffie_clarendon_3.pdf

  • Embrechts, P. and Höing, A. (2006): Extreme VaR scenarios in higher dimensions. Mimeo ETH Zürich.

    Google Scholar 

  • Embrechts, P., McNeil, A. and Straumann, D. (2002): Correlation and Dependence Properties in Risk Management: Properties and Pitfalls. In: Dempster, M. (Ed.): Risk Management: Value at Risk and Beyond. Cambridge University Press.

    Google Scholar 

  • Embrechts, P., Höing, A. and Juri, A. (2003): Using Copulae to bound the Value-at-Risk for functions of dependent risks. Finance & Stochastics 7, 145–167.

    Article  MATH  Google Scholar 

  • Embrechts, P., Furrer, H. and Kaufmann, R. (2008): Different Kinds of Risk. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T. (Eds.): Handbook of Financial Time Series, 729–751. Springer Verlag, New York.

    Google Scholar 

  • Engle, R.F. (1982): Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of UK Inflation. Econometrica 50, 987–1007.

    Article  MATH  MathSciNet  Google Scholar 

  • Engle, R.F. (2002): Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models. Journal of Business and Economic Statistics 20, 339–350.

    Article  MathSciNet  Google Scholar 

  • Engle, R.F. and Russell, J.R. (1998): Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data. Econometrica 66, 1127–1162.

    Article  MATH  MathSciNet  Google Scholar 

  • Erb, C.B., Harvey, C.R. and Viskanta, T.E. (1994): Forecasting International Equity Correlations. Financial Analysts Journal 50, 32–45.

    Article  Google Scholar 

  • Fermanian, J.-D. (2005): Goodness of fit tests for copulas. Journal of Multivariate Analysis 95, 119–152.

    Article  MATH  MathSciNet  Google Scholar 

  • Fermanian, J.-D. and Scaillet, O. (2003): Nonparametric estimation of copulas for time series. Journal of Risk 5, 25–54.

    Google Scholar 

  • Fermanian, J.-D. and Scaillet, O. (2005): Some statistical pitfalls in copula modeling for financial applications. In: Klein, E. (Ed.): Capital Formation, Governance and Banking. Nova Science Publishing.

    Google Scholar 

  • Fermanian, J.-D. and Wegkamp, M. (2004): Time dependent copulas. Mimeo, CREST.

    Google Scholar 

  • Fisher, R.A. (1932): Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.

    MATH  Google Scholar 

  • Frey, R. and McNeil, A.J. (2001): Modelling dependent defaults. ETH, Zürich, E-Collection, http://e-collection.ethbib.ethz.ch/show?type=bericht&nr=273

  • Gagliardini, P. and Gouriéroux, C. (2007a): An Efficient Nonparametric Estimator for Models with Non-linear Dependence. Journal of Econometrics 137, 187–229.

    Article  Google Scholar 

  • Gagliardini, P. and Gouriéroux, C. (2007b): Duration Time Series Models with Proportional Hazard. Journal of Time Series Analysis forthcoming.

    Google Scholar 

  • Galambos, J. (1978): The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.

    MATH  Google Scholar 

  • Garcia, R. and Tsafack, G. (2007): Dependence Structure and Extreme Comovements in International Equity and Bond Markets. Working paper, Université de Montreal.

    Google Scholar 

  • Genest, C. and Rivest, L.-P. (1993): Statistical Inference Procedures for Bivariate Archimedean Copulas. Journal of the American Statistical Association 88, 1034–1043.

    Article  MATH  MathSciNet  Google Scholar 

  • Genest, C., Ghoudi, K. and Rivest, L.-P. (1995): A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of Distributions. Biometrika 82, 543–552.

    Article  MATH  MathSciNet  Google Scholar 

  • Genest, C., Quasada Molina, J.J., Rodríguez Lallena, J.A. and Sempi, C. (1999): A characterization of quasi-copulas. Journal of Multivariate Analysis 69, 193–205.

    Article  MATH  MathSciNet  Google Scholar 

  • Genest, C., Rémillard, B. and Beaudoin, D. (2007): Goodness-of-Fit Tests for Copulas: A Review and Power Study. Insurance: Mathematics and Economics forthcoming.

    Google Scholar 

  • Giesecke, K. (2004): Correlated Default with Incomplete Information. Journal of Banking and Finance 28, 1521–1545.

    Article  Google Scholar 

  • Grammig, J., Heinen, A. and Rengifo, E. (2004): An analysis of the submission of orders on Xetra, using multivariate count data. CORE Discussion Paper 2004/58.

    Google Scholar 

  • Granger, C.W.J., Teräsvirta, T. and Patton, A.J. (2006): Common factors in conditional distributions for bivariate time series. Journal of Econometrics 132, 43–57.

    Article  MathSciNet  Google Scholar 

  • Hamilton, J.D. (1989): A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica 57, 357–384.

    Article  MATH  MathSciNet  Google Scholar 

  • Heinen, A. and Rengifo, E. (2003): Modelling Multivariate Time Series of Count Data Using Copulas. CORE Discussion Paper 2003/25.

    Google Scholar 

  • Hu, L. (2006): Dependence Patterns across Financial Markets: A Mixed Copula Approach. Applied Financial Economics 16, 717–729.

    Article  Google Scholar 

  • Hull, J. and White, A. (1998): Value–at–Risk when daily changes in market variables are not normally distributed. Journal of Derivatives 5, 9–19.

    Google Scholar 

  • Hurd, M., Salmon, M. and Schleicher, C. (2005): Using copulas to construct bivariate foreign exchange distributions with an application to the Sterling exchange rate index. Mimeo, Bank of England.

    Google Scholar 

  • Ibragimov, R. (2005): Copula-based dependence characterizations and modeling for time series. Harvard Institute of Economic Research Discussion Paper 2094.

    Google Scholar 

  • Ibragimov, R. (2006): Copula-based characterizations and higher-order Markov processes. Mimeo, Department of Economics, Harvard University.

    Google Scholar 

  • Joe, H. (1997): Multivariate Models and Dependence Concepts. Monographs in Statistics and Probability 73. Chapman and Hall, London.

    Google Scholar 

  • Joe, H. and Xu, J.J. (1996): The Estimation Method of Inference Functions for Margins for Multivariate Models. Working paper, Department of Statistics, University of British Columbia.

    Google Scholar 

  • Jondeau, E. and Rockinger, M. (2006): The copula-GARCH model of conditional dependencies: an international stock market application. Journal of International Money and Finance 25, 827–853.

    Article  Google Scholar 

  • Lee, L.-F. (1983): Generalized econometric models with selectivity Econometrica 51, 507–512.

    Article  MATH  MathSciNet  Google Scholar 

  • Lee, T.-H. and Long, X. (2005): Copula-based multivariate GARCH model with uncorrelated dependent standardized returns. Journal of Econometrics forthcoming.

    Google Scholar 

  • Li, D.X. (2000): On default correlation: a copula function approach. Journal of Fixed Income 9, 43–54.

    Google Scholar 

  • Longin, F. and Solnik, B. (2001): Extreme Correlation of International Equity Markets. Journal of Finance 56, 649–676.

    Article  Google Scholar 

  • Malevergne, Y. and Sornette, D. (2003): Testing the Gaussian Copula Hypothesis for Financial Assets Dependences. Quantitative Finance 3, 231–250.

    Article  MathSciNet  Google Scholar 

  • McNeil, A.J., Frey, R. and Embrechts, P. (2005): Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, New Jersey.

    MATH  Google Scholar 

  • Meitz M. and Saikkonen P. (2004): Ergodicity, mixing, and the existence of moments of a class of Markov models with applications to GARCH and ACD models. Econometric Theory forthcoming.

    Google Scholar 

  • Mikosch, T. (2006): Copulas: Tales and Facts, with discussion and rejoinder. Extremes 9, 3–62.

    Article  MathSciNet  Google Scholar 

  • Miller, D.J. and Liu, W.-H. (2002): On the recovery of joint distributions from limited information. Journal of Econometrics 107, 259–274.

    Article  MATH  MathSciNet  Google Scholar 

  • Mills, F.C. (1927): The Behavior of Prices. National Bureau of Economic Research, New York.

    Google Scholar 

  • Nelsen, R.B. (2006): An Introduction to Copulas, second Edition. Springer, New York.

    MATH  Google Scholar 

  • Newey, W.K. and McFadden, D. (1994): Large Sample Estimation and Hypothesis Testing. In: Engle, R.F. and McFadden, D. (Eds.): Handbook of Econometrics 4. North-Holland, Amsterdam.

    Google Scholar 

  • Okimoto, T. (2006): New evidence of asymmetric dependence structure in international equity markets: further asymmetry in bear markets: Journal of Financial and Quantitative Analysis forthcoming.

    Google Scholar 

  • Panchenko, V. (2005a): Goodness-of-fit Tests for Copulas. Physica A 355, 176–182.

    Article  MathSciNet  Google Scholar 

  • Panchenko, V. (2005b): Estimating and evaluating the predictive abilities of semiparametric multivariate models with application to risk management. Mimeo, University of Amsterdam.

    Google Scholar 

  • Patton, A.J. (2002): Applications of Copula Theory in Financial Econometrics. Unpublished Ph.D. dissertation, University of California, San Diego.

    Google Scholar 

  • Patton, A.J. (2004): On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation. Journal of Financial Econometrics 2, 130–168.

    Article  Google Scholar 

  • Patton, A.J. (2006a): Modelling Asymmetric Exchange Rate Dependence. International Economic Review 47, 527–556.

    Article  MathSciNet  Google Scholar 

  • Patton, A.J. (2006b): Estimation of Multivariate Models for Time Series of Possibly Different Lengths. Journal of Applied Econometrics 21, 147–173.

    Article  MathSciNet  Google Scholar 

  • Rivers, D. and Vuong, Q. (2002): Model Selection Tests for Nonlinear Dynamic Models. The Econometrics Journal 5, 1–39.

    Article  MATH  MathSciNet  Google Scholar 

  • Rodriguez, J.C. (2007): Measuring financial contagion: a copula approach. Journal of Empirical Finance 14, 401–423.

    Article  Google Scholar 

  • Rosenberg, J.V. (2003): Nonparametric pricing of multivariate contingent claims. Journal of Derivatives 10, 9–26.

    Article  Google Scholar 

  • Rosenberg, J.V. and Schuermann, T. (2006): A general approach to integrated risk management with skewed, fat-tailed risks. Journal of Financial Economics 79, 569–614.

    Article  Google Scholar 

  • Salmon, M. and Schleicher, C. (2006): Pricing Multivariate Currency Options with Copulas. In: Rank, J. (Ed.): Copulas: From Theory to Application in Finance. Risk Books, London.

    Google Scholar 

  • Sancetta, A. and Satchell, S. (2004): The Bernstein copula and its applications to modeling and approximations of multivariate distributions. Econometric Theory 20, 535–562.

    Article  MATH  MathSciNet  Google Scholar 

  • Scaillet, O. (2007): Kernel based goodness-of-fit tests for copulas with fixed smoothing parameters. Journal of Multivariate Analysis 98, 533–543.

    Article  MATH  MathSciNet  Google Scholar 

  • Schönbucher, P. and Schubert, D. (2001): Copula Dependent Default Risk in Intensity Models. Mimeo, Bonn University.

    Google Scholar 

  • Shih, J.H. and Louis, T.A. (1995): Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics 51, 1384–1399.

    Article  MATH  MathSciNet  Google Scholar 

  • Silvennoinen, A. and Teräsvirta, T. (2008): Multivariate GARCH Models. In: Andersen, T.G., Davis, R. A., Kreiss, J.-P. and Mikosch, T. (Eds.): Handbook of Financial Time Series, 201–229. Springer, New York.

    Google Scholar 

  • Sklar, A. (1959): Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut Statistique de l’Universite de Paris 8, 229–231.

    MathSciNet  Google Scholar 

  • Smith, M.D. (2003): Modelling sample selection using Archimedean copulas. Econometrics Journal 6, 99–123.

    Article  MATH  MathSciNet  Google Scholar 

  • Taylor, S.J. and Wang, Y.-H. (2004): Option prices and risk-neutral densities for currency cross-rates. Mimeo, Department of Accounting and Finance, Lancaster University.

    Google Scholar 

  • van den Goorbergh, R.W.J., C. Genest and Werker, B.J.M. (2005): Multivariate Option Pricing Using Dynamic Copula Models. Insurance: Mathematics and Economics 37, 101–114.

    Article  MATH  MathSciNet  Google Scholar 

  • van der Weide, R. (2002): GO-GARCH: A Multivariate Generalized Orthogonal GARCH Model. Journal of Applied Econometrics 17, 549–564.

    Article  Google Scholar 

  • Vuong, Q. (1989): Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses. Econometrica 57, 307–333.

    Article  MATH  MathSciNet  Google Scholar 

  • White, H. (1994): Estimation, Inference and Specification Analysis. Econometric Society Monographs 22, Cambridge University Press, Cambridge, U.K.

    Google Scholar 

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  1. Department of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford, Manor Road, Oxford OX1 3UQ, United Kingdom

    Andrew J. Patton

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    Patton, A.J. (2009). Copula–Based Models for Financial Time Series. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_34

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