arXiv subjects

Stanisław Drożdż

Publications and source records attributed to Stanisław Drożdż.

45 records · Page 3Linked to original sources

arXiv2016

Multifractal cross-correlation effects in two-variable time series of complex network vertex observables

We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased random walks. We consider three vertex properties that provide, respectively, short, medium, and long-range information regarding the topological role of vertices in a given network. In order to reveal the relation between these quantities, we applied the multifractal cross-correlation analysis technique, which provides information about the nonlinear effects in coupling of time series. We show that the considered network models are characterized by unique multifractal properties of the cross-correlation. In particular, it is possible to distinguish between Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks on the basis of fractal cross-correlation. Moreover, the analysis of protein contact networks reveals characteristics shared with both scale-free and small-world models.

physics.soc-ph↗

arXiv2016

World Financial 2014-2016 Market Bubbles: Oil Negative - US Dollar Positive

Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor $λ\approx 2$, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so called commodity currencies expressed in terms of the US dollar appears to take place with the oscillation pattern which largely is mirror reflected relative to oil price oscillation pattern. This documents recent strong anti-correlation between the dynamics of the oil price and of the USD. A related forecast made at the time of FENS 2015 conference (beginning of November) turned out to be quite satisfactory. These findings provide also further indication that such a log-periodically accelerating down-trend signals termination of the corresponding decreases.

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↗

arXiv2015

Quantifying origin and character of long-range correlations in narrative texts

In natural language using short sentences is considered efficient for communication. However, a text composed exclusively of such sentences looks technical and reads boring. A text composed of long ones, on the other hand, demands significantly more effort for comprehension. Studying characteristics of the sentence length variability (SLV) in a large corpus of world-famous literary texts shows that an appealing and aesthetic optimum appears somewhere in between and involves selfsimilar, cascade-like alternation of various lengths sentences. A related quantitative observation is that the power spectra S(f) of thus characterized SLV universally develop a convincing `1/f^beta' scaling with the average exponent beta =~ 1/2, close to what has been identified before in musical compositions or in the brain waves. An overwhelming majority of the studied texts simply obeys such fractal attributes but especially spectacular in this respect are hypertext-like, "stream of consciousness" novels. In addition, they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals. Scaling of S(f) in the present context implies existence of the long-range correlations in texts and appearance of multifractality indicates that they carry even a nonlinear component. A distinct role of the full stops in inducing the long-range correlations in texts is evidenced by the fact that the above quantitative characteristics on the long-range correlations manifest themselves in variation of the full stops recurrence times along texts, thus in SLV, but to a much lesser degree in the recurrence times of the most frequent words. In this latter case the nonlinear correlations, thus multifractality, disappear even completely for all the texts considered. Treated as one extra word, the full stops at the same time appear to obey the Zipfian rank-frequency distribution, however.

cs.CL↗

arXiv2015

Detecting and interpreting distortions in hierarchical organization of complex time series

Hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept. For model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric. Using the selected time series representing such diverse phenomena like price changes and inter-transaction times in the financial markets, sentence length variability in the narrative texts, Missouri River discharge and Sunspot Number variability as examples, we show that the resulting singularity spectra appear strongly asymmetric, more often left-sided but in some cases also right-sided. We present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying composition of the time series. One particularly intriguing case of this later kind of asymmetry is detected in the daily reported Sunspot Number variability. This signals that either the commonly used famous Wolf formula distorts the real dynamics in expressing the largest Sunspot Numbers or, if not, that their dynamics is governed by a somewhat different mechanism.

physics.data-an↗

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↗

arXiv2014

Detrended Cross-Correlation Analysis Consistently Extended to Multifractality

We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods like MF-DXA have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time, and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter $λ_q$. This relation provides information about character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.

physics.data-an↗

arXiv2012

Multifractal analysis of sentence lengths in English literary texts

This paper presents analysis of 30 literary texts written in English by different authors. For each text, there were created time series representing length of sentences in words and analyzed its fractal properties using two methods of multifractal analysis: MFDFA and WTMM. Both methods showed that there are texts which can be considered multifractal in this representation but a majority of texts are not multifractal or even not fractal at all. Out of 30 books, only a few have so-correlated lengths of consecutive sentences that the analyzed signals can be interpreted as real multifractals. An interesting direction for future investigations would be identifying what are the specific features which cause certain texts to be multifractal and other to be monofractal or even not fractal at all.

physics.data-an↗

arXiv2011

Computational approach to multifractal music

In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as physical processes called the 1/f (pink) noise. However, this is not true for classical music represented here by Frederic Chopin's works and for some jazz pieces that are much more correlated than the pink noise. We also perform a multifractal (MFDFA) analysis of these music pieces. We show that all the pieces reveal multifractal properties. The richest multifractal structures are observed for pop and rock music. Also the viariably of multifractal features is best visible for popular music genres. This can suggest that, from the multifractal perspective, classical and jazz music is much more uniform than pieces of the most popular genres of music.

physics.data-an↗