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Chaotic analysis of the foreign exchange rates. (English) Zbl 1120.91323

Summary: We investigate chaotic property of Foreign Exchange Rates of several countries. The foreign exchange market is a 24-h financial market. The trading in the foreign exchange markets generally involves the US dollar. Some of the related earlier works found evidence of chaotic structures in foreign exchange rates, some studies found little evidence of chaos, however, many of them showed evidence of nonlinear structure. This type of conflicting claims are common in nonlinear analyses of financial data, as shown in our earlier work (2006). For the present work, daily data were collected for twelve countries, mostly over the period January 1971 to December 2005. We have thus a time series of more than 8500 points for each country. Changes in the exchange rate are related to news in the fundamentals, but previous studies showed that the nature of the relation is nonlinear. We test the nonlinearity by the foreign exchange data by surrogate method and find different degree of nonlinearity for different countries. By measuring the largest Lyapunov exponent (LLE), we found indication of deterministic chaos in all exchange rate series. We attempted to find how foreign exchange relates to fundamental news like balance of payment to US dollar. Finally, we comment on limitation of LLE to report the dynamics of the time series.

MSC:

91B62 Economic growth models
91B64 Macroeconomic theory (monetary models, models of taxation)
37M10 Time series analysis of dynamical systems

Software:

Matlab
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Full Text: DOI

References:

[1] Bask, M., Dimensions, and Lyapunov exponents from exchange rate series, Chaos Solitons Fractals, 7, 12, 2199-2214 (1996)
[2] Bask, M., A positive Lyapunov exponent in Swedish exchange rates?, Chaos Solitons Fractals, 14, 5, 1295-1304 (2002) · Zbl 1071.91511
[3] P. Bacchetta, E. van Wincoop, Can information heterogeneity explain the exchange rate determination puzzle? NBER Working Paper 9498, 2003.; P. Bacchetta, E. van Wincoop, Can information heterogeneity explain the exchange rate determination puzzle? NBER Working Paper 9498, 2003.
[4] Das, A.; Das, P.; Roy, A. B., Nonlinear data analysis: a comparison between experimental [EEG] data and theoretical [ANN] data, Complexity, 7, 3, 30-40 (2002)
[5] Das, A.; Das, P., Does composite index of NYSE represents chaos in the long time scale?, Appl. Math. Comput., 174, 483-489 (2006) · Zbl 1137.91594
[6] Economic Research, Federal Reserve Bank of St. Louis and are free downloadable at <http://research.stlouisfed.org/fred2/categories/15> Visited March, 2006.; Economic Research, Federal Reserve Bank of St. Louis and are free downloadable at <http://research.stlouisfed.org/fred2/categories/15> Visited March, 2006.
[7] J. Faust, B. Rogers, S.-Yi, J. Wright, Time variation in the high-frequency response of exchange rates to macroeconomic announcements, Colloq. Int. de l’AEA, Marseille, March, 2003.; J. Faust, B. Rogers, S.-Yi, J. Wright, Time variation in the high-frequency response of exchange rates to macroeconomic announcements, Colloq. Int. de l’AEA, Marseille, March, 2003.
[8] De P. Grauwe, I. Vansteenkiste, Exchange rates and fundamentals A non-linear relationship? Center for Econ. Studies and Ifo Inst. for Econ. Res. Working Paper No. 577 Available from: <www.CESifo.de>, 2001. visited april 2006.; De P. Grauwe, I. Vansteenkiste, Exchange rates and fundamentals A non-linear relationship? Center for Econ. Studies and Ifo Inst. for Econ. Res. Working Paper No. 577 Available from: <www.CESifo.de>, 2001. visited april 2006.
[9] De P. Grauwe, M. Grimaldi, Intervention in the foreign exchange market in a model with noise traders, draft at University of Leuven, 2003.; De P. Grauwe, M. Grimaldi, Intervention in the foreign exchange market in a model with noise traders, draft at University of Leuven, 2003.
[10] Grauwe, De P.; Grimaldi, M., The exchange rate and its fundamentals in a complex world, Rev. Int. Econ., 13, 3, 549-575 (2005)
[11] Grauwe, De P.; Grimaldi, M., Exchange rate puzzles: a tale of switching attractors, Euro. Econ. Rev., 50, 1-33 (2006)
[12] LeBaron, B., Chaos and nonlinear forecastability in economics and finance, Phil. Trans. Royal Soc. London, Series A, 348, 397-404 (1994) · Zbl 0863.90032
[13] Lyons, R., The Microstructure Approach to Exchange Rates (2001), MIT press: MIT press Cambridge, MA
[14] MATLAB Release13, The MathWorks, Inc., 2002.; MATLAB Release13, The MathWorks, Inc., 2002.
[15] Obstfeld, M.; Rogoff, K., Foundations of International Macroeconomics (1996), MIT press: MIT press Cambridge, MA
[16] Parlitz, U., Nonlinear time series analysis, (Suykens, J. A.K.; Vandewalle, J., Nonlinear Modeling - Advanced Black-Box Techniques (1998), Kluwer Academic Publishers: Kluwer Academic Publishers Boston) · Zbl 0890.94033
[17] U. Parlitz, I. Wedekind, W. Lauterborn, C. Merkwirth, TSTOOL and User Manual, Ver. 1.11, DPI Göttingen, free download <www.physik3.gwdg.de/tstool/gpl.txt>, 2001.; U. Parlitz, I. Wedekind, W. Lauterborn, C. Merkwirth, TSTOOL and User Manual, Ver. 1.11, DPI Göttingen, free download <www.physik3.gwdg.de/tstool/gpl.txt>, 2001.
[18] Statistics: Country Data: Trade Balance, Foreign Trade Division, US Census Bureau, Washington at <http://www.census.gov/foreign-trade/balance/>, Visited April, 2006.; Statistics: Country Data: Trade Balance, Foreign Trade Division, US Census Bureau, Washington at <http://www.census.gov/foreign-trade/balance/>, Visited April, 2006.
[19] Theiler, J.; Eubank, S.; Longtin, A.; Galdrikian, B.; Farmer, J., Testing for nonlinearity in time series: the method of surrogated data, Physica D, 58, 77-94 (1992) · Zbl 1194.37144
[20] Wolf, A.; Swift, J. B.; Swinney, L. H.; Vastano, J. A., Determining Lyapunov exponent from a time series, Physica D, 16, 285-317 (1985) · Zbl 0585.58037
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