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Udovichenko, V. V.; Strizhak, P. E.

doi:10.1023/a:1020572016637

Cited by 15 publications

(12 citation statements)

References 4 publications

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“…The results for each process are averaged over its ten independent realizations in order to be statistically significant. In each case, the fractal analysis was performed by using MFDFA with the detrending polynomial of order m in the range (1,10). The results are shown in Figure 1.…”

Section: Analysis Of Fractional Brownian Motionmentioning

confidence: 99%

“…In recent years investigation of complex systems with regard to their fractal properties has become one of the elementary methods of such systems analysis [1]. Multifractal structures were identified in systems from various areas such as physics [2,3,4,5], biology [6,7,8], chemistry [9,10], economics [11,12,13] and even music [14,15,16,17,18]. A simple consequence of this fact is both popularization of the existing methods of multifractal analysis and proposing new, even more advanced methods.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Detrending on Multifractal Characteristics

et al. 2013

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

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Section: Analysis Of Fractional Brownian Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Detrending on Multifractal Characteristics

et al. 2013

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“…Multifractality constitutes a leading concept towards quantifying the related characteristics [4]. By now it finds applications in essentially all areas of the scientific activity including physics [5,6], biology [7-9], chemistry [10,11], geophysics [12,13], economics [14-21], hydrology [22], atmospheric physics [23], quantitative linguistics [24, 25], behavioral sciences [26], music [27,28], and even ecological sciences [29].At present the most efficient, numerically stable and precise [30] method to quantify multifractality is based on the Multifractal Detrended Fluctuation Analysis (MFDFA) [31]. Accordingly, for a discrete signal x(i) i=1,...,N one starts with the signal profile X(j) = j i=1 (x(i)− < x >), j = 1, ..., N , where < ... > denotes averaging over all i's.…”

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confidence: 99%

Detecting and interpreting distortions in hierarchical organization of complex time series

2015

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Hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept. For model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric. Using selected time series representing such diverse phenomena as price changes and intertransaction times in financial markets, sentence length variability in narrative texts, Missouri River discharge, and sunspot number variability as examples, we show that the resulting singularity spectra appear strongly asymmetric, more often left sided but in some cases also right sided. We present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying the composition of the time series. One particularly intriguing case of this latter kind of asymmetry is detected in the daily reported sunspot number variability. This signals that either the commonly used famous Wolf formula distorts the real dynamics in expressing the largest sunspot numbers or, if not, that their dynamics is governed by a somewhat different mechanism.

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“…Multifractal structures were identified in systems from various areas such as physics [2][3][4][5], biology [6][7][8], chemistry [9,10], economics [11][12][13] and even music [14][15][16][17][18][19]. One of the most popular methods of the multifractal analysis is multifractal detrended correlation (MFDFA) [20][21][22] and cross-correlation analysis (MFCCA) [23,24].…”

Section: Methodsmentioning

confidence: 99%

Quantitative Characteristics of Correlations of Meteorological Data

Rak

Bwanakare

2016

Acta Phys. Pol. A

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This paper presents the quantitative characteristics of correlations (and cross-correlations) of plant main ecofactors i.e. the ground and over-ground temperature, the wind speed, and the humidity. The study is based upon hourly data statistical observations collected in the region of Lublin, in Poland for the period 2001.05. 07-2009.04.10. This paper indicates that plant growth conditions constitute an emergent response to the above direct eco-factors. Then, the dynamics properties of each eco-factor is first analyzed alone for its multifractal structure. We apply the multifractal detrended correlation analysis and multifractal detrended cross-correlation analysis. We show that the widest multifractal spectrum is for over-ground temperature and the strongest power-law cross-correlations exist between ground and over-ground temperature. Next, an impulse response analysis is carried out to measure dynamical inter causalities within all the considered variables. As far as cross-impact between different eco-variables is concerned, one observes that the wind speed, the ground temperature and the air humidity dynamics are the most influenced, in terms of memory length time, by external temperature.

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Untitled

Cited by 15 publications

References 4 publications

Effect of Detrending on Multifractal Characteristics

Effect of Detrending on Multifractal Characteristics

Detecting and interpreting distortions in hierarchical organization of complex time series

Quantitative Characteristics of Correlations of Meteorological Data

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