31 research outputs found
Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach
We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the
Minimal Spanning Tree (MST) networks. We find the transition of the complex
network during its evolution from a (hierarchical) power law MST network,
representing the stable state of WSE before the recent worldwide financial
crash, to a superstar-like (or superhub) MST network of the market decorated by
a hierarchy of trees (being, perhaps, an unstable, intermediate market state).
Subsequently, we observed a transition from this complex tree to the topology
of the (hierarchical) power law MST network decorated by several star-like
trees or hubs. This structure and topology represent, perhaps, the WSE after
the worldwide financial crash, and could be considered to be an aftershock. Our
results can serve as an empirical foundation for a future theory of dynamic
structural and topological phase transitions on financial markets
Structural and topological phase transitions on the German Stock Exchange
We find numerical and empirical evidence for dynamical, structural and
topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in
the temporal vicinity of the worldwide financial crash. Using the Minimal
Spanning Tree (MST) technique, a particularly useful canonical tool of the
graph theory, two transitions of the topology of a complex network representing
FSE were found. First transition is from a hierarchical scale-free MST
representing the stock market before the recent worldwide financial crash, to a
superstar-like MST decorated by a scale-free hierarchy of trees representing
the market's state for the period containing the crash. Subsequently, a
transition is observed from this transient, (meta)stable state of the crash, to
a hierarchical scale-free MST decorated by several star-like trees after the
worldwide financial crash. The phase transitions observed are analogous to the
ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than
those found by Onnela-Chakraborti-Kaski-Kert\'esz for S&P 500 index in the
vicinity of Black Monday (October 19, 1987) and also in the vicinity of January
1, 1998. Our results provide an empirical foundation for the future theory of
dynamical, structural and topological phase transitions on financial markets
Complex Data: Mining Using Patterns
textabstractThere is a growing need to analyse sets of complex data, i.e., data in which the individual data items are (semi-) structured collections of data themselves, such as sets of time-series. To perform such analysis, one has to redefine familiar notions such as similarity on such complex data types. One can do that either on the data items directly, or indi- rectly, based on features or patterns computed from the individual data items. In this paper, we argue that wavelet decomposition is a general tool for the latter approac
Determination of the Hurst Exponent by Use of Wavelet Transforms
We propose a new method for (global) Hurst exponent determination based on
wavelets. Using this method, we analyze synthetic data with predefined Hurst
exponents, fracture surfaces and data from economy. The results are compared
with those obtained from Fourier spectral analysis. When many samples are
available, the wavelet and Fourier methods are comparable in accuracy. However,
when one or only a few samples are available, the wavelet method outperforms
the Fourier method by a large margin.Comment: 10 pages RevTeX, 13 Postscript figures. Some additional material
compared to previous versio
Taming Surprises
A methodological trajectory has been described dealing with the 'novelty' or 'surprise' issue in time series records arising from real world complex systems. It is based on extracting regularity (or scaling) characteristics of non-differentiable time series with wavelet transform, on modelling the complex system using multi-fractal properties and on investigating novelty in the context of the possible non-stationarity of such a model