Eur. Phys. J. B 4, 257-261 (1998)
https://doi.org/10.1007/s100510050376

Multi-affine analysis of typical currency exchange rates

SUPRAS, Institut de Physique B5, Université de Liège, 4000 Liège, Belgium

Corresponding author: ^a vandewal@gw.unipc.ulg.ac.be

Received: 25 September 1997
Revised: 13 January 1998
Accepted: 26 March 1998
Published online: 15 July 1998

Abstract

For foreign currency exchange rates, multi-affine analysis can put quantitatively into evidence the differences between correlated (daily closing market) values and random walks in time dependent data. The H(q) spectrum is presented and discussed here for the USD/DEM and JPY/USD exchange rates. The time-evolution of these ratios is found to be multi-affine. The -curve describing the hierarchy of exponents is numerically obtained. Our findings suggest that the modelling of exchange rate time-evolution from day to day is possible within the framework of modern statistical physics and related to models of turbulence in the physics of fluids. Finally, we argue that there is a multiplicity of information levels in the foreign exchange market such that the "efficient market theory" is a crude oversimplification indeed.