Detecting and interpreting distortions in hierarchical organization of complex time series

Dróżdż, S.; Oświęcimka, Paweł

doi:10.1103/physreve.91.030902

Cited by 126 publications

(73 citation statements)

References 42 publications

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“…The multifractal spectrum in this case is typically asymmetric (Drożdż and Oświęcimka, 2015). While under these conditions the crossover is not directly accessible to our SFD-based analysis, our additive model still allows for its characterization and offers an explanation for the asymmetry in D ( h ).…”

Section: Discussionmentioning

confidence: 99%

Decomposing Multifractal Crossovers

et al. 2017

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Physiological processes—such as, the brain's resting-state electrical activity or hemodynamic fluctuations—exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. Here, we present two methods to identify breakpoints or crossovers in multimodal multifractal scaling functions. These methods incorporate the robust iterative fitting approach of the focus-based multifractal formalism (FMF). The first approach (moment-wise scaling range adaptivity) allows for a breakpoint-based adaptive treatment that analyzes segregated scale-invariant ranges. The second method (scaling function decomposition method, SFD) is a crossover-based design aimed at decomposing signal constituents from multimodal scaling functions resulting from signal addition or co-sampling, such as, contamination by uncorrelated fractals. We demonstrated that these methods could handle multimodal, mono- or multifractal, and exact or empirical signals alike. Their precision was numerically characterized on ideal signals, and a robust performance was demonstrated on exemplary empirical signals capturing resting-state brain dynamics by near infrared spectroscopy (NIRS), electroencephalography (EEG), and blood oxygen level-dependent functional magnetic resonance imaging (fMRI-BOLD). The NIRS and fMRI-BOLD low-frequency fluctuations were dominated by a multifractal component over an underlying biologically relevant random noise, thus forming a bimodal signal. The crossover between the EEG signal components was found at the boundary between the δ and θ bands, suggesting an independent generator for the multifractal δ rhythm. The robust implementation of the SFD method should be regarded as essential in the seamless processing of large volumes of bimodal fMRI-BOLD imaging data for the topology of multifractal metrics free of the masking effect of the underlying random noise.

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Section: Discussionmentioning

confidence: 99%

Decomposing Multifractal Crossovers

et al. 2017

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“…Such effects of non-uniformity typically manifest themselves in an asymmetry of f (α), and furthermore may also be crucially informative regarding the content of a given time-series. A straightforward approach to quantifying this kind of asymmetry of f (α) is through the asymmetry parameter [44]:…”

Section: Fundamental Notions Of the Multifractal Formalismmentioning

confidence: 99%

Signatures of the Crypto-Currency Market Decoupling from the Forex

et al. 2019

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Based on the high-frequency recordings from Kraken, a cryptocurrency exchange and professional trading platform that aims to bring Bitcoin and other cryptocurrencies into the mainstream, the multiscale cross-correlations involving the Bitcoin (BTC), Ethereum (ETH), Euro (EUR) and US dollar (USD) are studied over the period between July 1, 2016 and December 31, 2018. It is shown that the multiscaling characteristics of the exchange rate fluctuations related to the cryptocurrency market approach those of the Forex. This, in particular, applies to the BTC/ETH exchange rate, whose Hurst exponent by the end of 2018 started approaching the value of 0.5, which is characteristic of the mature world markets. Furthermore, the BTC/ETH direct exchange rate has already developed multifractality, which manifests itself via broad singularity spectra. A particularly significant result is that the measures applied for detecting cross-correlations between the dynamics of the BTC/ETH and EUR/USD exchange rates do not show any noticeable relationships. This may be taken as an indication that the cryptocurrency market has begun decoupling itself from the Forex.

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“…Among the reasons behind the popularity of DFA was its ability of detecting fractal character of signals, which was subsequently extended to the multifractal case (the MFDFA method [17]), which also proved very useful if applied to empirical data [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], especially owing to its superior reliability if compared to other methods [37]. DCCA was also generalized in order to be applicable to signals with multifractal cross-correlations and the resulting MFDCCA/MFDXA algorithm [38] also attracted some attention [39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

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

2015

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The detrended cross-correlation coefficient ρDCCA 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 ρDCCA 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 ρDCCA that exploits the multifractal versions of DFA and DCCA: MFDFA and MFCCA, respectively. The resulting new coefficient ρq 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 ρq 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.

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Detecting and interpreting distortions in hierarchical organization of complex time series

Cited by 126 publications

References 42 publications

Decomposing Multifractal Crossovers

Decomposing Multifractal Crossovers

Signatures of the Crypto-Currency Market Decoupling from the Forex

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

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