Regensburg 2002 – wissenschaftliches Programm
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 12: Postersitzung
AKSOE 12.3: Poster
Montag, 11. März 2002, 16:00–18:00, D
Multitime correlations of financial data described by a Fokker-Planck-equation — •M. Karth, C. Renner, and J. Peinke — AG Hydrodynamik, FB Physik, Carl-von-Ossietzky-Universität Oldenburg
We present a stochastic analysis of a data set consisting of 106 quotes of the US Dollar - German Mark exchange rate, which gives access to multitime correlations. Evidence is given that the price changes x(τ) upon different delay times τ can be desribed as a Markov process evolving in τ. Thus, the dependence of the probability density function (pdf) p(x, τ) on the delay time τ can be described by a Fokker-Planck-equation, which also determines the explicit form of any general joint probability density function, finding price changes x(τ) for n different time scales τ. This represents an n-time-scale-correlation. The Fokker-Planck-equation is completely determined by two coefficients D1(x, τ) and D2(x, τ) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck-equation describe the empirical pdfs correctly, including the pronounced tails.