Influence of the maximal fluctuation moment order q on multifractal records normalized by finite-size effects

Pamuła, Grzegorz; Grech, Dariusz

doi:10.1209/0295-5075/105/50004

Cited by 18 publications

(9 citation statements)

References 29 publications

(26 reference statements)

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“…Since the seminal paper by Kantelhardt, et.al., [46] we know that multifractal properties one observes may appear not only as result of existing long-range nonlinear autocorrelations but also from the presence of fat tails in probability distributions of data or from linear autocorrelations present in shorter (finite) time series. The latter effect called also a finite size effect (FSE) has been extensively studied in quantitative way by various authors (see, e.g., [31,47,48,49,50,51]). In fact the mutual interaction and interplay between these three sources of multifractal effects leads to observable multifractal spectrum.…”

Section: Introductionmentioning

confidence: 99%

Quantitative approach to multifractality induced by correlations and broad distribution of data

Rak

Grech

2018

Physica A: Statistical Mechanics and its Applications

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We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from Levy regime up to those with finite variance. We use nonextensive Tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power-law decay for tails of probability distribution. The semi-analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of Tsallis parameterq and the scaling exponent β of the asymptotic decay of cumulated probability density function (CDF). The results are presented in Hurst and Hölder languages -more often used in study of multifractal phenomena. According to the provided semi-analytical relations, it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations, spurious multifractality generated by fat-tailed shape of distributions -eventually with their asymmetry, and the correction due to linear autocorrelations in analyzed time series of finite length. In particular, the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects. Examples from stock market data are presented to support these findings.

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Section: Introductionmentioning

confidence: 99%

Quantitative approach to multifractality induced by correlations and broad distribution of data

Rak

Grech

2018

Physica A: Statistical Mechanics and its Applications

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“…First, multifractality increases with the time series length and this pattern is rather uniform across all settings, which has not been so uniformly reported in other topical studies [26,27,43]. Second, the level of multifractality is not symmetrical around the zero correlation.…”

Section: Baseline Settingsmentioning

confidence: 65%

On Tail Dependence and Multifractality

Avdulaj

Krištoufek

2020

Mathematics

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We study whether, and if yes then how, a varying auto-correlation structure in different parts of distributions is reflected in the multifractal properties of a dynamic process. Utilizing the quantile autoregressive process with Gaussian copula using three popular estimators of the generalized Hurst exponent, our Monte Carlo simulation study shows that such dynamics translate into multifractal dynamics of the generated series. The tail-dependence of the auto-correlations forms strong enough non-linear dependencies to be reflected in the estimated multifractal spectra and separated from the case of the standard auto-regressive process. With a quick empirical example from financial markets, we argue that the interaction is more important for the asymmetric tail dependence. In addition, we discuss and explain the often reported paradox of higher multifractality of shuffled series compared to the original financial series. In short, the quantile-dependent auto-correlation structures qualify as sources of multifractality and they are worth further theoretical examination.

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“…e length of river levels is short and only about 800. For avoiding inaccurate results at large q caused by the finite-size effects [61][62][63][64], the q-range cannot be large. e range of q is chosen − 6 ≤ q ≤ 6 carefully.…”

Section: Multifractal Resultsmentioning

confidence: 99%

Joint Multifractal Analysis and Source Testing of River Level Records Based on Multifractal Detrended Cross-Correlation Analysis

Wang

Zhao

2020

Complexity

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The joint multifractal analysis is usually conducted in two different variables for their cross-correlations but rarely used for two records of one variable collected at two different places. It is important for the detection of change in multifractality in space. Besides, the cross-correlations in two analyzed series make the analysis of sources of joint multifractality difficult. There are few studies on the source of joint multifractality. We focus on the two issues for two level records at pairs of adjacent sites along one river and carry out an extension of our previous work which is about the single multifractality of one record with the same data set. The data set is collected from 10 observation stations of a northern China river and contains about two million high-frequency river level records. Results of joint multifractal analysis via multifractal detrended cross-correlation analysis show that the change in joint multifractality at pairs of adjacent sites caused by weak cross-correlations can be detected by comparing the single generalized Hurst exponent with the joint scaling exponent function and reveal the effects of human activities on joint multifractality. This analysis provides an approach for detecting the change in multifractality. Following the idea of our previous work, two robust hypothesis tests via a set of pairs of surrogate series are proposed for the source testing of joint multifractality. The analysis of the effects of cross-correlations is carried out via a proposed simultaneously half-shifting technique which can both minimize the cross-correlations between original series and make full use of records. Results of source analysis show not only the effects of autocorrelations in series and probability distribution of river levels but also the effects of cross-correlations between series.

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Influence of the maximal fluctuation moment order q on multifractal records normalized by finite-size effects

Cited by 18 publications

References 29 publications

Quantitative approach to multifractality induced by correlations and broad distribution of data

Quantitative approach to multifractality induced by correlations and broad distribution of data

On Tail Dependence and Multifractality

Joint Multifractal Analysis and Source Testing of River Level Records Based on Multifractal Detrended Cross-Correlation Analysis

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