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Power like scaling in Minimal Spanning Tree Graphs for FOREX networks

Andrzej Z. Górski 1Stanisław Drożdż 1,2Jarosław Kwapień 1Paweł Oświęcimka 1

1. Polish Academy of Sciences, Institute of Nuclear Physics (IFJ PAN), Radzikowskiego 152, Kraków 31-342, Poland
2. University of Rzeszów, Institute of Physics, Department of Complex Systems, Rejtana 16, Rzeszów 35-310, Poland

Abstract

The large set of 60 time series of daily foreign exchange (FX) rates from December 1998 to May 2005 is analyzed. The Minimal Spanning Tree (MST) graphs are constructed for all currencies taken as the base currency.  It is shown that the node rank (vertex multiplicity) for MSTs has power like, scale free behaviour. Taking into account that the rank values are always integers, we have found surprisingly good power like fits for great majority of base currencies. At the level of cumulative distributions the average scaling exponent oscillates around 1.5, the value often encountered in investigations of other complex systems. For the USD the power fit appears to be not so good as for the other base currencies and this effect can be well justified. The graph structure illustrates correlations between various currencies. Subtleties of the relation of graph structure and the power like node rank distribution to the currency cross correaltins are discussed. In particular, the special rule of the US dollar is clearly visible. In addition, other properties of corresponding correlation matrices are investigated, including the distribution of the correlation matrices' maximal eigenvalues.

 

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Related papers

Presentation: Oral at 3 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Andrzej Z. Górski
See On-line Journal of 3 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2007-09-10 18:00
Revised:   2009-06-07 00:44