We perform a comparative study of applicability the multifractal detrended fluctuation analysis (MFDFA) and wavelet transform modulus maxima (WTMM) method in proper detecting monofractal character data. quantify performance both methods by using different sorts artificial signals generated according to few well-known exactly soluble mathematical models: fractional Brownian motion, bifractal Lévy flights, binomial cascades. Our results show that majority situations which one does not know...

We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended and is able to properly identify quantify subtle characteristics cross-correlations between two time series. Our motivation for introducing this algorithm that already existing methods, like extension, have at best serious limitations most signals describing complex natural processes often indicate when there are none. The principal component present proper...

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and Wavelet Transform Modulus Maxima (WTMM) methods we investigate origin of multifractality in time series. Series fluctuating according to a qGaussian distribution, both uncorrelated correlated time, are used. For series at border (q=5/3) between Gaussian Levy basins attraction asymptotically find phase-like transition monofractal bifractal characteristics. This indicates that these may solely be specific nonlinear temporal...

The detrended cross-correlation coefficient ${\ensuremath{\rho}}_{\mathrm{DCCA}}$ has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, nonstationary time series. It is based and fluctuation analyses (DCCA DFA, respectively) can be viewed as an analog Pearson case analysis. works well many practical situations but by construction its applicability limited detection whether two signals are generally cross-correlated, without...

Social systems are characterized by an enormous network of connections and factors that can influence the structure dynamics these systems. Among them whole economical sphere human activity seems to be most interrelated complex. All financial markets, including youngest one, cryptocurrency market, belong this sphere. The complexity market studied from different perspectives. First, exchange rates other cryptocurrencies fiat currencies quantified means multifractal formalism. Second, coupling...

Based on the mathematical arguments formulated within multifractal detrended fluctuation analysis (MFDFA) approach it is shown that, in uncorrelated time series from Gaussian basin of attraction, effects resembling multifractality asymptotically disappear for positive moments when length increases. A hint given that this applies to negative as well and extends Lévy stable regime fluctuations. The related are also illustrated confirmed by numerical simulations. This documents genuine may only...

In this study the cross-correlations between cryptocurrency market represented by two most liquid and highest-capitalized cryptocurrencies: bitcoin ethereum, on one side, instruments representing traditional financial markets: stock indices, Forex, commodities, other are measured in period: January 2020-October 2022. Our purpose is to address question whether still preserves its autonomy with respect markets or it has already aligned them expense of independence. We motivated fact that some...

This contribution addresses the question commonly asked in scientific literature about sources of multifractality time series. Two primary are typically considered. These temporal correlations and heavy tails distribution fluctuations. Most often, they treated as two independent components, while true cannot occur without correlations. The distributions fluctuations affect span multifractal spectrum only when present. issues illustrated here using series generated by several model...

The complexity characteristics of texts written in natural languages are significantly related to the rules punctuation. In particular, distances between punctuation marks measured by number words quite universally follow family Weibull distributions known from survival analyses. However, values two parameters marking specific forms these distinguish languages. This is such a strong constraint that translated original language into another adopt quantitative target language. All changes take...

In relation to the traditional financial markets, cryptocurrency market is a recent invention and trading dynamics of all its components are readily recorded stored. This fact opens up unique opportunity follow multidimensional trajectory development since inception present time. Several main characteristics commonly recognized as stylized facts mature markets were quantitatively studied here. particular, it shown that return distributions, volatility clustering effects, even temporal...

A non-fungible token (NFT) market is a new trading invention based on the blockchain technology, which parallels cryptocurrency market. In present work, we study capitalization, floor price, number of transactions, inter-transaction times, and transaction volume value few selected popular collections. The results show that fluctuations all these quantities are characterized by heavy-tailed probability distribution functions, in most cases well described stretched exponentials, with trace...

We present a systematic study of various statistical characteristics high-frequency returns from the foreign exchange market. This is based on six rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It shown that rate return fluctuations for all pairs considered are well described by nonextensive statistics in terms q-Gaussians. There exist some small quantitative variations nonextensivity q-parameter values different this can be related to importance given world's currency trade....

Dierent variants of multifractal detrended uctuation analysis technique are applied in order to investigate various (articial and real-world) time series.Our shows that the calculated singularity spectra very sensitive detrending polynomial used within method.The relation between width spectrum (as well as Hurst exponent) calculation is evident.Furthermore, type this itself depends on kind analyzed signal.Therefore, such an can give us some extra information about correlative structure...

Time series of price returns for 80 the most liquid cryptocurrencies listed on Binance are investigated presence detrended cross-correlations. A spectral analysis correlation matrix and a topological minimal spanning trees calculated based this applied different positions moving window. The become more strongly cross-correlated among themselves than they used to be before. average cross-correlations increase with time specific scale in way that resembles Epps effect amplification when going...

We analyze tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. focus such quantities like the inter-transaction times, number of transactions in time unit, volume, and volatility. show that times long-range power-law autocorrelations. These lead to multifractality expressed by right-side asymmetry singularity spectra f(α) indicating periods increased market activity are characterized richer compared quiet market. also neither...

Magnetic field tomography (MFT) was used to extract estimates for distributed source activity from average and single trial MEG signals recorded while subjects identified objects (including faces) facial expressions of emotion.Regions interest (ROIs) were automatically the MFT solutions signal each subject.For one subject entire set obtained unaveraged data also compute simultaneous time series in different ROIs.Three pairs homologous areas hemisphere selected further analysis: posterior...

We consider a few quantities that characterize trading on stock market in fixed time interval: logarithmic returns, volatility, activity (i.e., the number of transactions), and volume traded. search for power-law cross-correlations among these aggregated over different units from 1 min to 10 min. Our study is based empirical data American consisting tick-by-tick recordings 31 stocks listed Dow Jones Industrial Average during years 2008-2011. Since all considered except returns show strong...