28 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
Modeling of super-extreme events: An application to the hierarchical Weierstrass-Mandelbrot Continuous-time Random Walk
We analytically demonstrate and numerically simulate two utmost cases of dragon-kings' impact on the (unnormalized) velocity autocorrelation function (VACF) of a complex time series generated by stochastic random walker. The first type of dragon-kings corresponds to a sustained drift whose duration time is much longer than that of any other event. The second type of dragon-kings takes the form of an abrupt shock whose amplitude velocity is much larger than those corresponding to any other event. The stochastic process in which the dragon-kings occur corresponds to an enhanced diffusion generated within the hierarchical Weierstrass-Mandelbrot Continuous-time Random Walk (WM-CTRW) formalism. Our analytical formulae enable a detailed study of the impact of the two super-extreme events on the VACF calculated for a given random walk realization on the form of upward deviations from the background power law decay present in the absence of dragon-kings. This allows us to provide a unambiguous distinction between the super-extreme dragon-kings and ‘normal' extreme "black swans”. The results illustrate diagnostic that could be useful for the analysis of extreme and super-extreme events in real empirical time serie
Fingered growth in channel geometry: A Loewner equation approach
A simple model of Laplacian growth is considered, in which the growth takes
place only at the tips of long, thin fingers. In a recent paper, Carleson and
Makarov used the deterministic Loewner equation to describe the evolution of
such a system. We extend their approach to a channel geometry and show that the
presence of the side walls has a significant influence on the evolution of the
fingers and the dynamics of the screening process, in which longer fingers
suppress the growth of the shorter ones
Predicting language diversity with complex network
Evolution and propagation of the world's languages is a complex phenomenon,
driven, to a large extent, by social interactions. Multilingual society can be
seen as a system of interacting agents, where the interaction leads to a
modification of the language spoken by the individuals. Two people can reach
the state of full linguistic compatibility due to the positive interactions,
like transfer of loanwords. But, on the other hand, if they speak entirely
different languages, they will separate from each other. These simple
observations make the network science the most suitable framework to describe
and analyze dynamics of language change. Although many mechanisms have been
explained, we lack a qualitative description of the scaling behavior for
different sizes of a population. Here we address the issue of the language
diversity in societies of different sizes, and we show that local interactions
are crucial to capture characteristics of the empirical data. We propose a
model of social interactions, extending the idea from, that explains the growth
of the language diversity with the size of a population of country or society.
We argue that high clustering and network disintegration are the most important
characteristics of models properly describing empirical data. Furthermore, we
cancel the contradiction between previous models and the Solomon Islands case.
Our results demonstrate the importance of the topology of the network, and the
rewiring mechanism in the process of language change
1996–2016: Two decades of econophysics: Between methodological diversification and conceptual coherence
Share Price Evolution as Stationary, Dependent Continuous-Time Random Walk
Simple model of share price evolution, which is an extension of Kehr-Kutner-Binder one and Montero-Masoliver models, is presented. The market empirical data inspired the assumptions of the model. The model seems to be the reference one for the study of the short-range correlations in financial data as it considers the observed correlation over two successive jumps of the financial ant
Intra-day variability of the stock market activity versus stationarity of the financial time series
In this paper we propose a new approach to a well-known phenomena of intra-day activity pattern on the stock market. We suggest that seasonality of inter-transaction times has a more significant impact than intra-day pattern of volatility. Our aim is not to remove the intra-day pattern from the data but to describe its impact on autocorrelation function estimators. We obtain an exact, analytical formula relating estimators of the autocorrelation functions of non-stationary (seasonal) process to its stationary counterpart. Hence, we prove that the day seasonality of inter-transaction times extends the memory of the process. That is, autocorrelation of both, price returns and their absolute values, relaxation to zero is longer