Chaos Theory and Application in Foreign Exchange Rates vs. IRR (Iranian Rial)

Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.

• M. A. Torkamani
• S. Mahmoodzadeh
• S. Pourroostaei
• C. Lucas

• Chaos
• Exchange Rate
• Nonlinear Models.

[1] B. Davies; "Exploring Chaos: Theory and Experiment (Studies in
Nonlinearity S.)", Westview Press, 2005.
[2] J. Banks, D. Valentina, J. Arthur; "Chaos: A Mathematical
Introduction", Cambridge University Press, 2003.
[3] W. Brock, P. Lima, "Nonlinear Time Series, Complexity Theory, and
Finance", Handbook of Statistics, Vol 14, Elsevier Science Publisher,
B.V. 1995.
[4] Y. Wu, D. Z. Zhang, "Demand fluctuation and chaotic behaviour by
interaction between customers and suppliers", Int. J. Production
Economics 107, 250-259, 2007.
[5] Julien Clinton Sprott; Chaos and Time-Series Analysis, Oxford
University Press - 2003.
[6] W. Barnett, P. Chen, "The Aggregation-Theoretic Monetary
Aggregates are Chaotic and Have Strange Attractors", Proceedings of
the Third International Symposium in Economic Theory and
Econometrics, Cambridge, Cambridge, University Press, 1987.
[7] P. Grassberger, I. Procaccia, "Measuring the Strangeness of Strange
Attractors", Physica. 9D, 30-31, 1983.
[8] S. Boccaletti, C. Grebogi, C. Lai, H. Mancini, D. Maza, "The control
of chaos: theory and applications", Physics Reports 329, 103-197,
2000.
[9] M. Shintani, O. Lintani, "Nonparametric Neural Network Estimation
of Lyapunov Exponents and a Direct Test for Chaos", Discussion
Paper, No. EM/02/434, 2002.
[10] H. Dewachter, M. Lyrio "The cost of technical trading rules in the
Forex market: A utility-based evaluation" International Money and
Finance, Vol.25, pp1072-1089, 2006.
[11] B. Davies; "Exploring Chaos: Theory and Experiment (Studies in
Nonlinearity S.)", Westview Press, 2005.
[12] W. Barnett, A. Serletis; "Martingales, nonlinearity, and chaos",
Journal of Economic Dynamics & Control 703-724, 2000.