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A Langevin equation for the rates of currency exchange based on the Markov analysis |
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| Authors: | F Farahpour A Bahraminasab GR Jafari F Ghasemi Muhammad Sahimi |
| Institution: | a Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran b Department of Physics, Lancaster University, Lancaster, LA14YB, UK c Department of Physics, Shahid Beheshti University, Evin, Tehran 19839, Iran d Department of Nano-Science, IPM, P.O. Box 19395-5531, Tehran, Iran e Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D 01187 Dresden, Germany f Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA g CNRS UMR 6529, Observatoire de la Côte d’Azur, BP 4229, 06304 Nice Cedex 4, France |
| Abstract: | We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D(1) and D(2), representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar. |
| Keywords: | Markov process Rates of exchange of various currencies Fluctuations Drift and diffusion coefficients |
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