Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals

Hedayatifar, Leila; Vahabi, M.; Jafari, G. R.

doi:10.1103/physreve.84.021138

Cited by 62 publications

(38 citation statements)

References 61 publications

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“…The altered DFT is then inverse Fourier transformed to generate a surrogate time series. The correlations in the surrogate series could be kept unchanged (for more detail see appendix (B) reference [16]), but the probability function changes to a Gaussian distribution [11,14,[16][17][18][19]. To obtain information about the effect of the phase randomization procedure on the PDF, one can also check the results of this procedure on the magnitude and sign series [15].…”

Section: Level Crossing Analysismentioning

confidence: 99%

Analysis of fractional Gaussian noises using level crossing method

Vahabi¹,

Jafari²,

Movahed³

2011

J. Stat. Mech.

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The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level crossing findings more sense. In this article, we calculated the average frequency of upcrossing for a wide range of fractional Gaussian noises from logarithmic (zero Hurst exponent, H = 0), to Gaussian, H = 1, (0 < H < 1). By introducing the relative change of the total numbers of upcrossings for original data with respect to so-called shuffled one, R, an empirical function for the Hurst exponent versus R has been established. Finally to make the concept more obvious, we applied this approach to some financial series.

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Section: Level Crossing Analysismentioning

confidence: 99%

Analysis of fractional Gaussian noises using level crossing method

Vahabi¹,

Jafari²,

Movahed³

2011

J. Stat. Mech.

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“…To this end, a multiscaling algorithm in the presence of unknown trends and noises is one of the most reliable approach introduced and implemented in many previous studies. Multifractal detrended fluctuation analysis (MF-DFA) [25] is a widely used technique to study the multifractal scaling properties of nonstationary time series [26][27][28][29][30]. MF-DFA is the generalization of the detrended fluctuation analysis (DFA) [31].…”

Section: A Multifractal Detrended Fluctuation Analysismentioning

confidence: 99%

Multiscaling behavior of atomic-scale friction

et al. 2017

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The scaling behavior of friction between rough surfaces is a well-known phenomenon. It might be asked whether such a scaling feature also exists for friction at an atomic scale despite the absence of roughness on atomically flat surfaces. Indeed, other types of fluctuations, e.g., thermal and instrumental fluctuations, become appreciable at this length scale and can lead to scaling behavior of the measured atomic-scale friction. We investigate this using the lateral force exerted on the tip of an atomic force microscope (AFM) when the tip is dragged over the clean NaCl (001) surface in ultra-high vacuum at room temperature. Here the focus is on the fluctuations of the lateral force profile rather than its saw-tooth trend; we first eliminate the trend using the singular value decomposition technique and then explore the scaling behavior of the detrended data, which contains only fluctuations, using the multifractal detrended fluctuation analysis. The results demonstrate a scaling behavior for the friction data ranging from 0.2 to 2 nm with the Hurst exponent H = 0.61 ± 0.02 at a 1σ confidence interval. Moreover, the dependence of the generalized Hurst exponent, h(q), on the index variable q confirms the multifractal or multiscaling behavior of the nanofriction data. These results prove that fluctuation of nanofriction empirical data has a multifractal behavior which deviates from white noise.

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“…Wang et al use multifractal detrended fluctuation analysis (MF‐DFA) to find the multifractal characteristics of pollution time series in Beijing, Zhengzhou, Jinan, and so on. The results of coupled trend fluctuation analysis (CDFA) 15 confirm the importance of oxides (SO 2 , NO 2 , CO) to urban pollution 16 . After combining MF‐DFA and detrended cross‐correlation analysis (DCCA), 17 Zhou proposes multifractal detrended cross‐correlation analysis (MF‐DCCA) 18 .…”

Section: Introductionmentioning

confidence: 82%

Study on the influence of surrounding urban SO₂, NO₂, and CO on haze formation in Beijing based on MF‐DCCA and boosting algorithms

Zhang

Chen

et al. 2020

Concurrency and Computation

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The formation of haze depends on the complex evolution behavior of SO 2 , NO 2 , and CO. We explore the influence of surrounding urban oxides on haze formation in Beijing. From the perspective of time evolution, multifractal detrended cross-correlation analysis (MF-DCCA) method quantitatively shows that all oxides reveal persistent cross-correlations (h xy : 0.640 sim; 0.995) in the short term and long term. The correlation characteristics of the same oxide in different regions are compared. In the short term, Zhangjiakou (SO 2 /NO 2) and Tianjin (CO) have the strongest multifractal features, while Zhangjiakou (SO 2 /NO 2 /CO) is more prominent in the long term. Their sources are mainly Fat-tailed. Ignoring the characteristics of timing, the fitting degree (R 2) of LightGBM model to PM2.5 concentration regression is 0.862 after the addition of neighboring oxides, an increase of 2.0%. CatBoost's R 2 improves by 6.4%. The feature importance score indicates that Langfang's SO 2 and Chengde's CO contribute the most to the formation of PM2.5. This study has certain reference value for the formulation of oxide emission strategy in the surrounding area of Beijing.

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Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals

Cited by 62 publications

References 61 publications

Analysis of fractional Gaussian noises using level crossing method

Analysis of fractional Gaussian noises using level crossing method

Multiscaling behavior of atomic-scale friction

Study on the influence of surrounding urban SO₂, NO₂, and CO on haze formation in Beijing based on MF‐DCCA and boosting algorithms

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Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals

Cited by 62 publications

References 61 publications

Analysis of fractional Gaussian noises using level crossing method

Analysis of fractional Gaussian noises using level crossing method

Multiscaling behavior of atomic-scale friction

Study on the influence of surrounding urban SO2, NO2, and CO on haze formation in Beijing based on MF‐DCCA and boosting algorithms

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Product

Resources

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Study on the influence of surrounding urban SO₂, NO₂, and CO on haze formation in Beijing based on MF‐DCCA and boosting algorithms