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Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula

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  • Patton, Andrew J

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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Bibliographic Info

Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt01q7j1s2.

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Date of creation: 01 Jun 2001
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Handle: RePEc:cdl:ucsdec:qt01q7j1s2

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Keywords: time series; copulas; exchange rates; dependence;

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Cited by:
  1. Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J, 2002. "Common Factors in Conditional Distributions," University of California at San Diego, Economics Working Paper Series qt3bd1n1x5, Department of Economics, UC San Diego.
  2. 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.
  3. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies.
  4. Sorge, Marco & Virolainen, Kimmo, 2006. "A comparative analysis of macro stress-testing methodologies with application to Finland," Journal of Financial Stability, Elsevier, vol. 2(2), pages 113-151, June.
  5. Bodnar, Taras & Hautsch, Nikolaus, 2013. "Copula-based dynamic conditional correlation multiplicative error processes," CFS Working Paper Series 2013/19, Center for Financial Studies (CFS).
  6. 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.
  7. Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA.
  8. Marco Sorge, 2004. "Stress-testing financial systems: an overview of current methodologies," BIS Working Papers 165, Bank for International Settlements.
  9. 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.
  10. 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.

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