arXiv subjects

Paweł Oświȩcimka

Publications and source records attributed to Paweł Oświȩcimka.

5 recordsLinked to original sources

arXiv2019

Multifractal cross-correlations between the World Oil and other Financial Markets in 2012-2017

Statistical and multiscaling characteristics of WTI Crude Oil prices expressed in US dollar in relation to the most traded currencies as well as to gold futures and to the E-mini S$\&$P500 futures prices on 5 min intra-day recordings in the period January 2012 - December 2017 are studied. It is shown that in most of the cases the tails of return distributions of the considered financial instruments follow the inverse cubic power law. The only exception is the Russian ruble for which the distribution tail is heavier and scales with the exponent close to 2. From the perspective of multiscaling the analysed time series reveal the multifractal organization with the left-sided asymmetry of the corresponding singularity spectra. Even more, all the considered financial instruments appear to be multifractally cross-correlated with oil, especially on the level of medium-size fluctuations, as the multifractal cross-correlation analysis carried out by means of the multifractal cross-correlation analysis (MFCCA) and detrended cross-correlation coefficient $ρ_q$ show. The degree of such cross-correlations is however varying among the financial instruments. The strongest ties to the oil characterize currencies of the oil extracting countries. Strength of this multifractal coupling appears to depend also on the oil market trend. In the analysed time period the level of cross-correlations systematically increases during the bear phase on the oil market and it saturates after the trend reversal in 1st half of 2016. The same methodology is also applied to identify possible causal relations between considered observables. Searching for some related asymmetry in the information flow mediating cross-correlations indicates that it was the oil price that led the Russian ruble over the time period here considered rather than vice versa.

q-fin.ST↗

arXiv2018

Dynamical variety of shapes in financial multifractality

The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves to evaluation of whether or not a time series is multifractal and width of the resulting singularity spectrum is considered a measure of the degree of complexity involved. However, the character of the complexity of time series generated by the natural processes usually appears much more intricate than such a bare statement can reflect. As an example, based on the long-term records of S&P500 and NASDAQ - the two world leading stock market indices - the present study shows that they indeed develop the multifractal features, but these features evolve through a variety of shapes, most often strongly asymmetric, whose changes typically are correlated with the historically most significant events experienced by the world economy. Relating at the same time the index multifractal singularity spectra to those of the component stocks that form this index reflects the varying degree of correlations involved among the stocks.

q-fin.ST↗

arXiv2017

Right-side-stretched multifractal spectra indicate small-worldness in networks

Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features observed in real-world systems: i) local clustering and ii) the possibility to move across a network by means of long-range links that significantly reduce the characteristic path length. A natural question would be whether there exist several "types" of small-world architectures, giving rise to a continuum of models with properties (partially) shared with other models belonging to different network families. Here, we take advantage of the interplay between network theory and time series analysis and propose to investigate small-world signatures in complex networks by analyzing multifractal characteristics of time series generated from such networks. In particular, we suggest that the degree of right-sided asymmetry of multifractal spectra is linked with the degree of small-worldness present in networks. This claim is supported by numerical simulations performed on several parametric models, including prototypical small-world networks, scale-free, fractal and also real-world networks describing protein molecules. Our results also indicate that right-sided asymmetry emerges with the presence of the following topological properties: low edge density, low average shortest path, and high clustering coefficient.

physics.data-an↗

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↗

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↗