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Study of Nonlinearities in the Dynamics of Exchange Rates: Is There Any Evidence of Chaos?

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  • Vitaliy Vandrovych

    ()
    (International Business School Brandeis University)

Abstract

This paper studies the dynamics of six major exchange rates, and runs formal tests to distinguish among different types of nonlinearities. In particular we study exchange rate returns, normalized exchange rates and exchange rate volatilities, classifying these series using BDS test, correlation dimensions and maximum Liapunov exponents. Estimates of dimension indicate high complexity in all series, suggesting that the series are either stochastic processes or high dimensional deterministic processes. Though we obtain a number of positive estimates of Liapunov exponent, they are quite small and it seems more appropriate to interpret them as indicating stochastic origin of the series.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 234.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:234

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  1. Mototsugu Shintani & Oliver Linton, 2002. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," LSE Research Online Documents on Economics 2093, London School of Economics and Political Science, LSE Library.
  2. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
  3. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July.
  4. Mototsugu Shintani & Oliver Linton, 2003. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 331-357, February.
  5. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619.
  6. Gilmore, Claire G., 2001. "An examination of nonlinear dependence in exchange rates, using recent methods from chaos theory," Global Finance Journal, Elsevier, vol. 12(1), pages 139-151.
  7. Barnett, William A. & Serletis, Apostolos, 2000. "Martingales, nonlinearity, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 703-724, June.
  8. Bask, Mikael, 2000. "A Positive Lyapunov Exponent in Swedish Exchange Rates?," UmeÃ¥ Economic Studies 528, Umeå University, Department of Economics.
  9. Brzozowska-Rup, Katarzyna & Orłowski, Arkadiusz, 2004. "Application of bootstrap to detecting chaos in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 317-321.
  10. repec:att:wimass:9520 is not listed on IDEAS
  11. Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, EconWPA.
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