World currency exchange rate cross-correlations

World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rates within the basket of 60 currencies in the period December 1998 -- May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the perspective of a peripheral currency. This largest eigenvalue is seen to systematically decrease and thus the structure of correlations becomes more heterogeneous, when more significant currencies are used as reference. An extreme case in this later respect is the USD in the period considered. Besides providing further insight into subtle nature of complexity, these observations point to a formal procedure that in general can be used for practical purposes of measuring the relative currencies significance on various time horizons.Comment: 4 pages, 3 figures, LaTe

Scale free effects in world currency exchange network

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed -- like the USD case -- towards more compact MST topology can be observed when correlations increase.Comment: Eur. Phys. J. B (2008) in pres

Are the contemporary financial fluctuations sooner converging to normal?

Based on the tick-by-tick price changes of the companies from the U.S. and from the German stock markets over the period 1998-99 we reanalyse several characteristics established by the Boston Group for the U.S. market in the period 1994-95, which serves to verify their space and time-translational invariance. By increasing the time scales we find a significantly more accelerated crossover from the power-law (alpha approximately 3) asymptotic behaviour of the distribution of returns towards a Gaussian, both for the U.S. as well as for the German stock markets. In the latter case the crossover is even faster. Consistently, the corresponding autocorrelation functions of returns and of the time averaged volatility also indicate a faster loss of memory with increasing time. This route towards efficiency may reflect a systematic increase of the information processing when going from past to present.Comment: 14 pages, revised versio

Different fractal properties of positive and negative returns

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(\alpha)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding H\"{o}lder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.Comment: presented at FENS2007 conference, 8 pages, 4 Fig