Fourier-detrended fluctuation analysis

Chianca, Vito; Ticona, Armando; Penna, T. J. P.

doi:10.1016/j.physa.2005.03.047

Cited by 84 publications

(58 citation statements)

References 16 publications

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“…To eliminate the effect of sinusoidal trend, we apply the Fourier Detrended Fluctuation Analysis (F-DFA) [12,13]. After elimination of the trend we use the Multifractal Detrended Fluctuation Analysis (MF-DFA) to analysis the data set.…”

Section: Introductionmentioning

confidence: 99%

Multifractal detrended fluctuation analysis of sunspot time series

et al. 2006

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We use multifractal detrended fluctuation analysis (MF-DFA), to See query 1 study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation function. We discuss how the existence of the crossover timescales is related to a sinusoidal trend. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The Hurst exponent of the time series without the sinusoidal trend is 0.12 ± 0.01. Also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to long range correlations.

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Section: Introductionmentioning

confidence: 99%

Multifractal detrended fluctuation analysis of sunspot time series

et al. 2006

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“…To date, the performance of the zeroth order DMA algorithm (DMA 0 ) has been extensively studied [28][29][30][31][32][33]. Conversely, the fundamental properties of the higherorder DMA (DMA m with m ≥ 1) have not been completely investigated [14].…”

Section: Detrending Moving Average Algorithmmentioning

confidence: 99%

Detrending moving average algorithm: Frequency response and scaling performances

Carbone

Kiyono

2016

Phys. Rev. E

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The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or highdimensional arrays) either over time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent and finite scale range behavior will be discussed.

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“…Although the MF-DFA and MF-DXA methods eliminate the polynomial trends, the sinusoidal trends remain [47,48]. There are several robust methods to eliminate the sinusoidal one such as Fourier Detrended Fluctuations Analysis (F-DFA) [62,64], which is actually a high-pass filter, and Singular Value Decomposition (SVD) [65,66]. One of the most disadvantage of the F-DFA method is the reduction of the size of underlying data set.…”

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

132

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We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, (12 − 24) ≤ s ≤ 130 months, is λ = 1.17 ± 0.04 which is almost similar for all underlying rivers at 1σconfidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ ∈ (0.76, 0.85) and γ× ∈ (0.30, 0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), λ ≈ (hsun + hriver)/2 is confirmed.

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Fourier-detrended fluctuation analysis

Cited by 84 publications

References 16 publications

Multifractal detrended fluctuation analysis of sunspot time series

Multifractal detrended fluctuation analysis of sunspot time series

Detrending moving average algorithm: Frequency response and scaling performances

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

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