arXiv subjects

Pawel Oswiecimka

Publications and source records attributed to Pawel Oswiecimka.

13 recordsLinked to original sources

arXiv2018

High-dimensional dynamics in a single-transistor oscillator containing Feynman-Sierpinski resonators: effect of fractal depth and irregularity

Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic dynamics even in the context of an elementary, single-transistor oscillator circuit. Sierpiński gaskets of variable depth are constructed using discrete capacitors and inductors, whose values are scaled according to a simple sequence. It is found that in regular fractals of this kind each iteration effectively adds a conjugate pole/zero pair, yielding gradually more complex and broader frequency responses, which can also be implemented as much smaller Foster equivalent networks. The resonators are instanced in the circuit as one-port devices, replacing the inductors found in the initial version of the oscillator. By means of a highly simplified numerical model, it is shown that increasing the fractal depth elevates the dimension of the chaotic dynamics, leading to high-order hyperchaos. This result is overall confirmed by SPICE simulations and experiments, which however also reveal that the non-ideal behavior of physical components hinders obtaining high-dimensional dynamics. The issue could be practically mitigated by building the Foster equivalent networks rather than the verbatim fractals. Furthermore, it is shown that considerably more complex resonances, and consequently richer dynamics, can be obtained by rendering the fractal resonators irregular through reshuffling the inductors, or even by inserting a limited number of focal imperfections. The present results draw attention to the potential usefulness of fractal resonators for generating high-dimensional chaotic dynamics, and underline the importance of irregularities and component non-idealities.

nlin.CD↗

arXiv2018

Apparent remote synchronization of amplitudes: a demodulation and interference effect

A form of "remote synchronization" was recently described wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and mutual information, synchronization and causality dip at a certain distance, then recover before eventually fading. Here, the underlying mechanism is finally elucidated through novel experiments and simulations. The system non-linearity is found to have a dual role: it supports chaotic dynamics, and it enables energy exchange between the lower and higher sidebands of a predominant frequency. This frequency acts as carrier signal in an arrangement resembling standard amplitude modulation, wherein the lower sideband and the demodulated baseband signals spectrally overlap. Due to a spatially-dependent phase relationship, at a certain distance near-complete destructive interference occurs between them, causing the observed dip. Methods suitable for detecting non-trivial entrainment, such as transfer entropy and the auxiliary system approach, nevertheless reveal that synchronization and causality actually decrease with distance monotonically. Remoteness is, therefore, arguably only apparent, as also reflected in the propagation of external perturbations. These results demonstrate a complex mechanism of dynamical interdependence, and exemplify how it can lead to incorrectly inferring synchronization and causality.

nlin.CD↗

arXiv2017

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

Based on a recently proposed $q$-dependent detrended cross-correlation coefficient $ρ_q$, we generalize the concept of minimum spanning tree (MST) by introducing a family of $q$-dependent minimum spanning trees ($q$MST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales. They inherit this ability directly from the coefficients $ρ_q$ that are processed here to construct a distance matrix. Conventional MST with detrending corresponds in this context to $q=2$. We apply the $q$MSTs to sample empirical data from the stock market and discuss the results. We show that the $q$MST graphs can complement $ρ_q$ in disentangling correlations that cannot be observed by the MST graphs based on $ρ_{\rm DCCA}$ and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest. We apply our method to data from the stock market and obtain more information about correlation structure of the data than by using $q=2$ only. We show that two sets of signals that differ from each other statistically can give comparable trees for $q=2$, while only by using the trees for $q \ne 2$ we become able to distinguish between these sets. We also show that a family of $q$MSTs for a range of $q$ express the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different $q$s. Our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry.

q-fin.ST↗

arXiv2015

Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations

The detrended cross-correlation coefficient $ρ_{\rm DCCA}$ has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analogue of the Pearson coefficient in the case of the fluctuation analysis. The coefficient $ρ_{\rm DCCA}$ works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations. In order to introduce some related flexibility, here we propose an extension of $ρ_{\rm DCCA}$ that exploits the multifractal versions of DFA and DCCA: MFDFA and MFCCA, respectively. The resulting new coefficient $ρ_q$ not only is able to quantify the strength of correlations, but also it allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. We show how the coefficient $ρ_q$ works in practical situations by applying it to stochastic time series representing processes with long memory: autoregressive and multiplicative ones. Such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence, so we are convinced that this new measure can successfully be applied in time series analysis. In particular, we present an example of such application to highly complex empirical data from financial markets. The present formulation can straightforwardly be extended to multivariate data in terms of the $q$-dependent counterpart of the correlation matrices and then to the network representation.

physics.data-an↗

arXiv2015

Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies

We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 min to 10 min. Our study is based on empirical data from the American stock market consisting of tick-by-tick recordings of 31 stocks listed in Dow Jones Industrial Average during the years 2008-2011. Since all the considered quantities except the returns show strong daily patterns related to the variable trading activity in different parts of a day, which are the best evident in the autocorrelation function, we remove these patterns by detrending before we proceed further with our study. We apply the multifractal detrended cross-correlation analysis with sign preserving (MFCCA) and show that the strongest power-law cross-correlations exist between trading activity and volume traded, while the weakest ones exist (or even do not exist) between the returns and the remaining quantities. We also show that the strongest cross-correlations are carried by those parts of the signals that are characterized by large and medium variance. Our observation that the most convincing power-law cross-correlations occur between trading activity and volume traded reveals the existence of strong fractal-like coupling between these quantities.

q-fin.ST↗

arXiv2015

Modeling the average shortest path length in growth of word-adjacency networks

We investigate properties of evolving linguistic networks defined by the word-adjacency relation. Such networks belong to the category of networks with accelerated growth but their shortest path length appears to reveal the network size dependence of different functional form than the ones known so far. We thus compare the networks created from literary texts with their artificial substitutes based on different variants of the Dorogovtsev-Mendes model and observe that none of them is able to properly simulate the novel asymptotics of the shortest path length. Then, we identify the local chain-like linear growth induced by grammar and style as a missing element in this model and extend it by incorporating such effects. It is in this way that a satisfactory agreement with the empirical result is obtained.

cs.CL↗

arXiv2013

Stock returns versus trading volume: is the correspondence more general?

This paper presents a quantitative analysis of the relationship between the stock market returns and corresponding trading volumes using high- frequency data from the Polish stock market. First, for stocks that were traded for suffciently long period of time, we study the return and volume distributions and identify their consistency with the power-law functions. We find that, for majority of stocks, the scaling exponents of both distri- butions are systematically related by about a factor of 2 with the ones for the returns being larger. Second, we study the empirical price impact of trades of a given volume and find that this impact can be well described by a square-root dependence: r(V) V^(1/2). We conclude that the prop- erties of data from the Polish market resemble those reported in literature concerning certain mature markets.

q-fin.ST↗

arXiv2010

The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect.

q-fin.ST↗

arXiv2010

Quantitative features of multifractal subtleties in time series

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated series at the border (q=5/3) between the Gaussian and the Levy basins of attraction asymptotically we find a phase-like transition between monofractal and bifractal characteristics. This indicates that these may solely be the specific nonlinear temporal correlations that organize the series into a genuine multifractal hierarchy. For analyzing various features of multifractality due to such correlations, we use the model series generated from the binomial cascade as well as empirical series. Then, within the temporal ranges of well developed power-law correlations we find a fast convergence in all multifractal measures. Besides of its practical significance this fact may reflect another manifestation of a conjectured q-generalized Central Limit Theorem.

physics.data-an↗

arXiv2009

World stock market: more sizeable trend reversal likely in February/March 2010

Based on our "finance-prediction-oriented" methodology which involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble" we analyze the 2009 world stock market (here represented by the SP500, Hang Seng and WIG) development. We identify elements that indicate the third decade of September 2009 as a time limit for the present bull market phase which is thus to be followed by a significant correction. In this context we also interpret the Chinese stock market index SSE. The third decade of September 2009 was accompanied with a stock market correction typically within the range of 4-5% worldwide. Taking into account the market patterns that followed the time of delivering the previous scenario we present an updated scenario whose critical time corresponds to October 28, 2009. Assuming quite evident (as of November 12, 2009) termination of the correction due to the above critical time we extend - consistently with our methodology - the stock market forecasting scenario. The corresponding expected SP500 future trend is shown in Fig. 5 and it supports a potential average continuation of increases to as far into the future as the turn of February/March 2010. We also indicate the log-periodic patterns on the gold market and they point to the end of November 2009 as the time when the trend reversal - likely local however - is expected to begin.

q-fin.ST↗

arXiv2008

Criticality Characteristics of Current Oil Price Dynamics

Methodology that recently lead us to predict to an amazing accuracy the date (July 11, 2008) of reverse of the oil price up trend is briefly summarized and some further aspects of the related oil price dynamics elaborated. This methodology is based on the concept of discrete scale invariance whose finance-prediction-oriented variant involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble". From this perspective the present (as of August 22, 2008) violent - but still log-periodically decelerating - decrease of the oil prices is associated with the decay of such a "super- bubble" that has started developing about one year ago on top of the longer-term oil price increasing phase (normal bubble) whose ultimate termination is evaluated to occur in around mid 2010.

q-fin.ST↗

arXiv2008

Current log-periodic view on future world market development

Applicability of the concept of financial log-periodicity is discussed and encouragingly verified for various phases of the world stock markets development in the period 2000-2010. In particular, a speculative forecasting scenario designed in the end of 2004, that properly predicted the world stock market increases in 2007, is updated by setting some more precise constraints on the time of duration of the present long-term equity market bullish phase. A termination of this phase is evaluated to occur in around November 2009. In particular, on the way towards this dead-line, a Spring-Summer 2008 increase is expected. On the precious metals market a forthcoming critical time signal is detected at the turn of March/April 2008 which marks a tendency for at least a serious correction to begin. In the present extended version some predictions for the future oil price are incorporated. In particular a serious correction on this market is expected to start in the coming days.

q-fin.ST↗

arXiv2006

Wavelet versus Detrended Fluctuation Analysis of multifractal structures

We perform a comparative study of applicability of the Multifractal Detrended Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM) method in proper detecting of mono- and multifractal character of data. We quantify the performance of both methods by using different sorts of artificial signals generated according to a few well-known exactly soluble mathematical models: monofractal fractional Brownian motion, bifractal Levy flights, and different sorts of multifractal binomial cascades. Our results show that in majority of situations in which one does not know a priori the fractal properties of a process, choosing MFDFA should be recommended. In particular, WTMM gives biased outcomes for the fractional Brownian motion with different values of Hurst exponent, indicating spurious multifractality. In some cases WTMM can also give different results if one applies different wavelets. We do not exclude using WTMM in real data analysis, but it occurs that while one may apply MFDFA in a more automatic fashion, WTMM has to be applied with care. In the second part of our work, we perform an analogous analysis on empirical data coming from the American and from the German stock market. For this data both methods detect rich multifractality in terms of broad f(alpha), but MFDFA suggests that this multifractality is poorer than in the case of WTMM.

cond-mat.other↗