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Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula

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Andrew J. Patton

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Abstract

Linear correlation is only an adequate means of describing the dependence between two random variables when they are jointly elliptically distributed. When the joint distribution of two or more variables is not elliptical the linear correlation coefficient becomes just one of many possible ways of summarising the dependence structure between the variables. In this paper we make use of a theorem due to Sklar (1959), which shows that an n-dimensional distribution function may be decomposed into its n marginal distributions, and a copula, which completely describes the dependence between the n variables. We verify that Sklar's theorem may be extended to conditional distributions, and apply it to the modelling of the time-varying joint distribution of the Deutsche mark - U.S. dollar and Yen - U.S. dollar exchange rate returns. We find evidence that the conditional dependence between these exchange rates is time-varying, and that it is asymmetric: dependence is greater during appreciations of the U.S. dollar against the mark and the yen than during depreciations of the U.S. dollar. We also find strong evidence of a structural break in the conditional copula following the introduction of the euro.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2001-09.

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Date of creation: Jun 2001
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Handle: RePEc:cdl:ucsdec:2001-09

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  1. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August. [Downloadable!] (restricted)
  2. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
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  5. Jeremy Berkowitz, 1999. "Evaluating the forecasts of risk models," Finance and Economics Discussion Series 1999-11, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  6. Kling, John L & Bessler, David A, 1989. "Calibration-Based Predictive Distributions: An Application of Prequential Analysis to Interest Rates, Money, Prices, and Output," Journal of Business, University of Chicago Press, vol. 62(4), pages 477-99, October. [Downloadable!] (restricted)
  7. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  8. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series 99-20, Department of Economics, UC San Diego. [Downloadable!]
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  9. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York. [Downloadable!]
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  1. Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J., 2002. "Common factors in conditional distributions," Working Paper Series in Economics and Finance 515, Stockholm School of Economics.
    Other versions:
  2. Xiaohong Chen & Yanqin Fan, 2002. "Evaluating Density Forecasts via the Copula Approach," Working Papers 0225, Department of Economics, Vanderbilt University, revised Sep 2003. [Downloadable!]
  3. Xiaohong Chen & Yanqin Fan, 2002. "Estimation of Copula-Based Semiparametric Time Series Models," Working Papers 0226, Department of Economics, Vanderbilt University, revised Oct 2004. [Downloadable!]
  4. Andrew J. Patton, 2001. "Estimation of Copula Models for Time Series of Possibly Different Lengths," University of California at San Diego, Economics Working Paper Series 2001-17, Department of Economics, UC San Diego. [Downloadable!]
  5. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2006. "A Multivariate Integer Count Hurdle Model: Theory and Application to Exchange Rate Dynamics," CoFE Discussion Paper 06-06, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  6. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
  7. Yanqin Fan & Xiaohong Chen, 2004. "Estimation of Copula-Based Semiparametric Time Series Models," Econometric Society 2004 Far Eastern Meetings 559, Econometric Society. [Downloadable!]
  8. Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA. [Downloadable!]
  9. Rachel Campbell & Catherine S. Forbes & Kees Koedijk & Paul Kofman, 2003. "Diversification Meltdown or the Impact of Fat tails on Conditional Correlation?," Monash Econometrics and Business Statistics Working Papers 18/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  10. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2007. "An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics," CoFE Discussion Paper 07-04, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  11. Xiaohong Chen & Yanqin Fan, 2004. "Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification," Working Papers 0419, Department of Economics, Vanderbilt University, revised Sep 2004. [Downloadable!]
  12. Jesus Gonzalo & Jose Olmo, 2005. "Contagion Versus Flight To Quality In Financial Markets," Economics Working Papers we051810, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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