Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis

Nagarajan, Radhakrishnan; Kavasseri, Rajesh G.

doi:10.1016/j.chaos.2005.01.036

Cited by 38 publications

(40 citation statements)

References 13 publications

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“…As of the importance of investigating trends and probably removing them from series, one can point out to two following aims: I) In some cases, there exists one or more crossover (time) scales, s × , in the log-log plot of F q (s) versus s (equation (6)), segregating regimes with different scaling exponents. These patterns demonstrates that underlying fluctuation has different correlation behavior in various values of scales [47,48,65,66,71]. II) In many cases, crossovers are produced by the embedded sinusoidal trends, e.g.…”

Section: B Singular Value Decomposition (Svd)mentioning

confidence: 99%

“…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%

“…Using the SVD method not only we can track the influence of sinusoidal trends on the results, but also the synchronization of two underlying data sets will be guaranteed [65,66]. In addition, we can determine over which scale, noises or trends have dominant contribution also the value of so-called crossover in the fluctuation function, in terms of the scale is computed by using DCCA method.…”

Section: B Singular Value Decomposition (Svd)mentioning

confidence: 99%

“…To apply the MF-DXA (see the following subsection), we have to synchronize two underlying data set which may not be done using the F-DFA method. On the other hand, the SVD method promises to remain the length as well as synchronization [65,66]. Here in order to eliminate the effect of sinusoidal trends, we apply the Singular Value Decomposition (SVD) [65,66].…”

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

“…On the other hand, the SVD method promises to remain the length as well as synchronization [65,66]. Here in order to eliminate the effect of sinusoidal trends, we apply the Singular Value Decomposition (SVD) [65,66]. After trends elimination, we use the MF-DXA to analyze the cleaned data sets.…”

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

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

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

133

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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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Section: B Singular Value Decomposition (Svd)mentioning

confidence: 99%

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

Section: B Singular Value Decomposition (Svd)mentioning

confidence: 99%

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

Section: Analysis Techniques and Data Descriptionmentioning

confidence: 99%

See 3 more Smart Citations

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

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

133

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Markov Properties of Electrical Discharge Current Fluctuations in Plasma

et al. 2011

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Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal's coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyal's coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyal's coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references, figures and major correction

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Characteristics and Multifractal Properties of Daily Streamflow in a Semiarid Environment

Emadi

Khalili

Movahed

2016

Iran. J. Sci. Technol.Trans. Civ. Eng.

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Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis

Cited by 38 publications

References 13 publications

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

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

Markov Properties of Electrical Discharge Current Fluctuations in Plasma

Characteristics and Multifractal Properties of Daily Streamflow in a Semiarid Environment

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