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


  • Vitaliy Vandrovych

    () (International Business School Brandeis University)


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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  • Vitaliy Vandrovych, 2005. "Study of Nonlinearities in the Dynamics of Exchange Rates: Is There Any Evidence of Chaos?," Computing in Economics and Finance 2005 234, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:234

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    References listed on IDEAS

    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-337, July.
    3. 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.
    4. 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.
    5. Bask, Mikael, 2000. "A Positive Lyapunov Exponent in Swedish Exchange Rates?," Umeå Economic Studies 528, Umeå University, Department of Economics.
    6. 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 339-368, July.
    7. 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.
    8. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    9. Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, EconWPA.
    10. 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.
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications

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