440 research outputs found
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
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
Accuracy analysis of the box-counting algorithm
Accuracy of the box-counting algorithm for numerical computation of the
fractal exponents is investigated. To this end several sample mathematical
fractal sets are analyzed. It is shown that the standard deviation obtained for
the fit of the fractal scaling in the log-log plot strongly underestimates the
actual error. The real computational error was found to have power scaling with
respect to the number of data points in the sample (). For fractals
embedded in two-dimensional space the error is larger than for those embedded
in one-dimensional space. For fractal functions the error is even larger.
Obtained formula can give more realistic estimates for the computed generalized
fractal exponents' accuracy.Comment: 3 figure
Decay of Nuclear Giant Resonances: Quantum Self-similar Fragmentation
Scaling analysis of nuclear giant resonance transition probabilities with
increasing level of complexity in the background states is performed. It is
found that the background characteristics, typical for chaotic systems lead to
nontrivial multifractal scaling properties.Comment: 4 pages, LaTeX format, pc96.sty + 2 eps figures, accepted as: talk at
the 8th Joint EPS-APS International Conference on Physics Computing (PC'96,
17-21. Sept. 1996), to appear in the Proceeding
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
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
Asymmetric random matrices: What do we need them for?
Complex systems are typically represented by large ensembles of observations.
Correlation matrices provide an efficient formal framework to extract
information from such multivariate ensembles and identify in a quantifiable way
patterns of activity that are reproducible with statistically significant
frequency compared to a reference chance probability, usually provided by
random matrices as fundamental reference. The character of the problem and
especially the symmetries involved must guide the choice of random matrices to
be used for the definition of a baseline reference. For standard correlation
matrices this is the Wishart ensemble of symmetric random matrices. The real
world complexity however often shows asymmetric information flows and therefore
more general correlation matrices are required to adequately capture the
asymmetry. Here we first summarize the relevant theoretical concepts. We then
present some examples of human brain activity where asymmetric time-lagged
correlations are evident and hence highlight the need for further theoretical
developments
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