Finite sample properties of power-law cross-correlations estimators

Krištoufek, Ladislav

doi:10.1016/j.physa.2014.10.068

Cited by 21 publications

(11 citation statements)

References 53 publications

(78 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our results derived from the main analytical pipeline are supported by further analysis accounting for the slightly different length of analyzed signals from the task states ( Supplementary Material ). Because the multifractal profile of a time series is influenced by its length ( Grech and Pamuła, 2012 ; Rak and Grech, 2018 ), we anticipated a similar effect on our bivariate multifractal analysis ( Kristoufek, 2015b ); thus, we re-analyzed our dataset in a pipeline adjusted to the different lengths of analyzed pair of time series based on the different response times. The results agree with our primary analysis, indicating that the slightly varying signal length had no effect on the observed patterns.…”

Section: Discussionmentioning

confidence: 99%

Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

Stylianou

Racz

Kim

et al. 2021

Front. Hum. Neurosci.

View full text Add to dashboard Cite

The human brain consists of anatomically distant neuronal assemblies that are interconnected via a myriad of synapses. This anatomical network provides the neurophysiological wiring framework for functional connectivity (FC), which is essential for higher-order brain functions. While several studies have explored the scale-specific FC, the scale-free (i.e., multifractal) aspect of brain connectivity remains largely neglected. Here we examined the brain reorganization during a visual pattern recognition paradigm, using bivariate focus-based multifractal (BFMF) analysis. For this study, 58 young, healthy volunteers were recruited. Before the task, 3-3 min of resting EEG was recorded in eyes-closed (EC) and eyes-open (EO) states, respectively. The subsequent part of the measurement protocol consisted of 30 visual pattern recognition trials of 3 difficulty levels graded as Easy, Medium, and Hard. Multifractal FC was estimated with BFMF analysis of preprocessed EEG signals yielding two generalized Hurst exponent-based multifractal connectivity endpoint parameters, H(2) and ΔH15; with the former indicating the long-term cross-correlation between two brain regions, while the latter captures the degree of multifractality of their functional coupling. Accordingly, H(2) and ΔH15 networks were constructed for every participant and state, and they were characterized by their weighted local and global node degrees. Then, we investigated the between- and within-state variability of multifractal FC, as well as the relationship between global node degree and task performance captured in average success rate and reaction time. Multifractal FC increased when visual pattern recognition was administered with no differences regarding difficulty level. The observed regional heterogeneity was greater for ΔH15 networks compared to H(2) networks. These results show that reorganization of scale-free coupled dynamics takes place during visual pattern recognition independent of difficulty level. Additionally, the observed regional variability illustrates that multifractal FC is region-specific both during rest and task. Our findings indicate that investigating multifractal FC under various conditions – such as mental workload in healthy and potentially in diseased populations – is a promising direction for future research.

show abstract

Section: Discussionmentioning

confidence: 99%

Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

Stylianou

Racz

Kim

et al. 2021

Front. Hum. Neurosci.

View full text Add to dashboard Cite

show abstract

“…It is worthwhile to note that short length N of the investigated series or small scale s often results in a spurious detection of multifractal behavior from a monofractal model [19]. To evaluate the finite-size effect [25] Fig. 11.…”

Section: Binomial Multifractal Seriesmentioning

confidence: 99%

“…Since detrended fluctuation analysis (DFA) has been proposed by Peng et al [3] to detect the long-range power-law correlations in DNA sequences, it has been successfully applied to diverse fields [4][5][6][7][8][9][10][11]. Then Podobnik and Stanley [12] generalized DFA and introduced the detrended cross-correlation analysis (DCCA) for two non-stationary time series, which has aroused increasing interest in analysis of long-range cross-correlation and multifractality [1,[13][14][15][16][17][18][19][20][21][22][23][24][25]. Specifically, the analysis is based on the bivariate Hurst exponent h xy estimation, which is related to an asymptotic power-law decay of the cross-correlation function.…”

Section: Introductionmentioning

confidence: 99%

“…A power-law cross-correlated process has the cross-correlation function C xy (k) ∝ k 2hxy−2 for k → +∞ and the cross-power spectrum | f xy (s)| ∝ s 1−2hxy for s → 0+. h xy = 0.5 is characteristic for the absence of power-law cross-correlation, while processes with h xy > 0.5 are cross-persistent and h xy < 0.5 indicates the anti-persistent cross-correlation of the data [2,12,25]. Basis of these, the cross-correlation coefficient (σ DCCA ) was introduced with the objective of quantifying the level of cross-correlation between nonstationary time series [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Weighted multifractal cross-correlation analysis based on Shannon entropy

Xiong

Shang

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

a b s t r a c tIn this paper, we propose a modification of multifractal cross-correlation analysis based on statistical moments (MFSMXA) method, called weighted MFSMXA method based on Shannon entropy (W-MFSMXA), to investigate cross-correlations and cross-multifractality between time series. Robustness of this method is verified by numerical experiments with both artificial and stock returns series. Results show that the proposed W-MFSMXA method not only keep the multifractal structure unchanged, but contains more significant information of series compared to the previous MFSMXA method. Furthermore, analytic formulas of the binomial multifractal model are generated for W-MFSMXA. Theoretical analysis and finite-size effect test demonstrate that W-MFSMXA slightly outperforms MFSMXA for relatively shorter series. We further generate the scaling exponent ratio to describe the relation of two methods, whose profile is found approximating a centrosymmetric hyperbola. Cross-multifractality is found in returns series but then destroyed after being shuffled as a consequence of the removed long memory in separate series.

show abstract

“…To obtain the cross-correlation between two nonstationary series, DFA was extended to the detrended cross-correlation analysis (DCCA) [16]. By defining scale-dependent detrended fluctuation functions, the methods of DFA and DCCA together with their extensions have been applied in a wide range of disciplines [17,18,19,20,21,22,23,24,25,26,27,28,29,30]. Since the ordinary least squares (OLS) method expresses the estimated parameters of standard regression framework as a form of variances and covariances, it builds a bridge between the regression framework and the family of DFA/DCCA as the latter can also produce variances and covariances.…”

Section: Introductionmentioning

confidence: 99%

A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities

Wang

Chen

2018

Sci Rep

View full text Add to dashboard Cite

On the basis of detrended fluctuation analysis (DFA), we propose a new bivariate linear regression model. This new model provides estimators of multi-scale regression coefficients to measure the dependence between variables and corresponding variables of interest with multi-scales. Numerical tests are performed to illustrate that the proposed DFA-bsaed regression estimators are capable of accurately depicting the dependence between the variables of interest and can be used to identify different dependence at different time scales. We apply this model to analyze the PM2.5 series of three adjacent cities (Beijing, Tianjin, and Baoding) in Northern China. The estimated regression coefficients confirmed the dependence of PM2.5 among the three cities and illustrated that each city has different influence on the others at different seasons and at different time scales. Two statistics based on the scale-dependent t-statistic and the partial detrended cross-correlation coefficient are used to demonstrate the significance of the dependence. Three new scale-dependent evaluation indices show that the new DFA-based bivariate regression model can provide rich information on studied variables.

show abstract

Finite sample properties of power-law cross-correlations estimators

Cited by 21 publications

References 53 publications

Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

Weighted multifractal cross-correlation analysis based on Shannon entropy

A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities

Contact Info

Product

Resources

About