arXiv subjects

Robert Gębarowski

Publications and source records attributed to Robert Gębarowski.

7 recordsLinked to original sources

arXiv2020

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Hölder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.

physics.data-an↗

arXiv2019

Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis

Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high frequency exchange rates of eight major world currencies over 2010-2018 period are used to study cross-correlations. The study is motivated by fundamental questions in complex systems' response to significant environmental changes and by potential applications in investment strategies, including detecting triangular arbitrage opportunities. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. However hierarchical organization of ties expressed in terms of dendrograms, with a novel application of the multiscale cross-correlation coefficient, are more pronounced at large fluctuations. The cross-correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relations. Some pairs from outside triangular relations are however identified to be exceptionally strongly correlated as compared to the average strength of triangular correlations.This in particular applies to those exchange rates that involve Australian and New Zealand dollars and reflects their economic relations. Significant events with impact on the Forex are shown to induce triangular arbitrage opportunities which at the same time reduce cross--correlations on the smallest time scales and act destructively on the multiscale organization of correlations. In 2010--2018 such instances took place in connection with the Swiss National Bank intervention and the weakening of British pound sterling accompanying the initiation of Brexit procedure. The methodology could be applicable to temporal and multiscale pattern detection in any time series.

q-fin.ST↗

arXiv2018

Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects

Based on 1-minute price changes recorded since year 2012, the fluctuation properties of the rapidly-emerging Bitcoin (BTC) market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst exponents and multiscaling effects. The findings are compared to the stylized facts of mature world markets. While early trading was affected by system-specific irregularities, it is found that over the months preceding Apr 2018 all these statistical indicators approach the features hallmarking maturity. This can be taken as an indication that the Bitcoin market, and possibly other cryptocurrencies, carry concrete potential of imminently becoming a regular market, alternative to the foreign exchange (Forex). Since high-frequency price data are available since the beginning of trading, the Bitcoin offers a unique window into the statistical characteristics of a market maturation trajectory.

q-fin.ST↗

arXiv2015

Multiscaling edge effects in an agent-based money emergence model

An agent-based computational economical toy model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied. The model considered, while manageable, is significantly complex, however. It is already able to reveal phenomena that can be interpreted as emergence and collapse of money as well as the related competition effects. In particular, it is shown that - as an extra emerging effect - the money lifetimes near the critical threshold value develop multiscaling, which allow one to set parallels to critical phenomena and, thus, to the real financial markets.

q-fin.ST↗

arXiv2014

Transport in two-dimensional quantum wires with point scatterers. The Wigner-Smith time delay

Electronic transport properties of the disordered quantum wires are considered. The disorder is introduced via impurities (point scatterers), distributed uniformly over the two-dimensional strip, which represents a model quantum wire. Incident electrons with a given energy are scattered on impurities and boundaries of the wire. The electron-electron interaction is neglected in the model. In particular, the intermediate regime and the localization regime of transport are studied in more detail in terms of the conductance and statistical properties of S-matrix ensemble for a given incident electron energy. The Wigner-Smith time delay distribution obtained for the localization regime is compared with the prediction for the scattering by a one-dimensional random potential.

cond-mat.mes-hall↗

arXiv2014

Submilisecond acoustic pulses: effective pitch and Weber-Fechner law in discrimination of duration times

The enclosed tests demonstrate that an effective pitch can be attributed to acoustic signals shorter then tenths of milliseconds. A power-law dependence of this pitch on the signal's duration time is found for subjects tested with Gaussian pulses. The discrimination threshold for the pulse duration time reported on the basis of the effective pitch increases proportionally to the duration time itself, i.e. it follows the Weber-Fechner law. A model based on the "Helmholtz's harp" idea, i.e. a series of damped resonators tuned in the audible range of frequencies, reveals the mechanism of producing a maximum in the filtered spectrum of the pulse. This corroborates the power law in the dependence of the position of the maximum on the duration time of the pulse. The model indicates a possibility of designing a manmade device dedicated to determination of the durations so short that they are inaccessible by direct measurements.

physics.class-ph↗

arXiv2014

Competition of Commodities for the Status of Money in an Agent-based Model

In this model study of the commodity market, we present some evidence of competition of commodities for the status of money in the regime of parameters, where emergence of money is possible. The competition reveals itself as a rivalry of a few (typically two) dominant commodities, which take the status of money in turn.

q-fin.ST↗