arXiv subjects

Rafał Rak

Publications and source records attributed to Rafał Rak.

7 recordsLinked to original sources

arXiv2026

Visibility graphs can make money in financial markets

Traditional technical analysis indicators, although widely used by market participants, are often not sufficiently effective. We propose the Visibility Graphs Relative Strength Index (VGRSI), based on backward visibility relations in the price of a financial instrument. Rescaled to the 0--100 range, it can generate profitable trading signals. The performance of the indicator was evaluated using an automated trading strategy based on a 30-day optimisation window and a 7-day test window for three instruments representing different asset classes: DJI30, EUR/USD and XAU/USD over the 2024--2025 period (503 trading days). The strategy based on VGRSI signals generated a profit of USD~146,000 for DJI30, USD~69,000 for EUR/USD, and USD~125,000 for XAU/USD. This gives a total result of USD$\sim$340,000, which corresponds to an average profit of USD$\sim$676 per trading day, with a fixed investment of USD~1,000 to open a single trade. For all three assets, the strategy generated substantial profits while maintaining a moderate drawdown (10--18\% relative to a portfolio value of USD~10,000), a relatively low trading intensity (3.3--4.8 trades per day) and high Sharpe ratio values (2.55--3.6). These results indicate that VGRSI constitutes a promising technical analysis tool that goes beyond the classical trend-following approach by exploiting the geometric properties of asset price fluctuations.

cs.CE↗

arXiv2024

Quantifying multifractal anisotropy in two dimensional objects

An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA) into 2D. It is tested on synthetic structures to ensure its effectiveness, with results indicating consistency. The interdisciplinary potential of this method in describing real surfaces and images is demonstrated, revealing previously unknown directional multifractality in data sets from the Martian surface and the Crab Nebula. The multifractal characteristics of Jackson Pollock's paintings are also analyzed. The results point to their evolution over the time of creation of these works.

physics.app-ph↗

arXiv2020

The Fractional Preferential Attachment Scale-Free Network Model

Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment}, we propose a generalisation of the Barabási--Albert model---the 'Fractional Preferential Attachment' (FPA) scale-free network model---that generates networks with time-independent degree distributions $p(k)\sim k^{-γ}$ with degree exponent $2<γ\leq3$ (where $γ=3$ corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the $f$ parameter, where $f \in (0,1\rangle$. Depending on the different values of $f$ parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on $f$, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that $f$ parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of $f$, FPA networks are not fractal.

physics.soc-ph↗

arXiv2019

Universal features of mountain ridge networks on Earth

Compared to the heavily studied surface drainage systems, the mountain ridge systems have been a subject of less attention even on the empirical level, despite the fact that their structure is richer. To reduce this deficiency, we analyze different mountain ranges by means of a network approach and grasp some essential features of the ridge branching structure. We also employ a fractal analysis as it is especially suitable for describing properties of rough objects and surfaces. As our approach differs from typical analyses that are carried out in geophysics, we believe that it can initialize a research direction that will allow to shed more light on the processes that are responsible for landscape formation and will contribute to the network theory by indicating a need for the construction of new models of the network growth as no existing model can properly describe the ridge formation. We also believe that certain features of our study can offer help in the cartographic generalization. Specifically, we study structure of the ridge networks based on the empirical elevation data collected by SRTM. We consider mountain ranges from different geological periods and geographical locations. For each mountain range, we construct a simple topographic network representation (the ridge junctions are nodes) and a ridge representation (the ridges are nodes and the junctions are edges) and calculate the parameters characterizing their topology. We observe that the topographic networks inherit the fractal structure of the mountain ranges but do not show any other complex features. In contrast, the ridge networks, while lacking the proper fractality, reveal the power-law degree distributions with the exponent $1.6\le β\le 1.7$. By taking into account the fact that the analyzed mountains differ in many properties, these values seem to be universal for the earthly mountainous terrain.

physics.geo-ph↗

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↗

arXiv2015

Route to chaos in generalized logistic map

Motivated by a possibility to optimize modelling of the population evolution we postulate a generalization of the well-know logistic map. Generalized difference equation reads: \begin{equation} x_{n+1}=rx^p_n(1-x^q_n), \end{equation} $x\in[0,1],\;(p,q)>0,\;n=0,1,2,...$, where the two new parameters $p$ and $q$ may assume any positive values. The standard logistic map thus corresponds to the case $p=q=1$. For such a generalized equation we illustrate the character of the transition from regularity to chaos as a function of $r$ for the whole spectrum of $p$ and $q$ parameters. As an example we consider the case for $p=1$ and $q=2$ both in the periodic and chaotic regime. We focus on the character of the corresponding bifurcation sequence and on the quantitative nature of the resulting attractor as well as its universal attribute (Feigenbaum constant).

nlin.CD↗

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↗