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Paper   IPM / Nano-Sciences / 8683
School of Nano Science
  Title:   A Langevin equation for the rates of currency exchange based on the Markov analysis
1.  F. Farahpour
2.  Z. Eskandari
3.  A. Bahraminasab
4.  Gholam Reza Jafari
5.  F. Ghasemi
6.  Muhammad Sahimi
7.  M. R. Rahimi Tabar
  Status:   Published
  Journal: Physica A
  No.:  2
  Vol.:  385
  Year:  2007
  Pages:   9
  Publisher(s):   Elsevier B.V.
  Supported by:  IPM
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 aMarkov 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 exchangerates that we analyze. We derive an effective Langevinequation 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

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