Effects of non-stationarity on the magnitude and sign scaling in the multi-scale vertical velocity increment

Li, Qinglei; Fu, Zuntao; Yuan, Naiming; Xie, Fenghua

doi:10.1016/j.physa.2014.05.004

Cited by 17 publications

(12 citation statements)

References 42 publications

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“…2c and d show that the PRS procedure affect the results of non-stationary time series more significantly than these of stationary ones. This is consistent with the conclusion that nonlinearity is more notable in non-stationary vertical wind velocity [52]. Lastly, after extracting the large-scale fluctuations through EMD method in both time series, the variations of the first digit distribution with scales become similar for both stationary and non-stationary time series, as shown in Fig.…”

Section: First Digit Distributions Of Multi-scale Increment Seriessupporting

confidence: 88%

“…These un-established equilibrium motions cause the interaction between motions of very large scales and small scales [5], and they lead to nonstationarity in the scale regimes analyzed here. Better understanding and quantifying non-stationarity is crucial to explore atmosphere boundary-layer at very stable conditions, especially through time series analysis methods [2,5,6,9,10,52].…”

Section: Discussionmentioning

confidence: 99%

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Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law

2016

Communications in Nonlinear Science and Numerical Simulation

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Section: First Digit Distributions Of Multi-scale Increment Seriessupporting

confidence: 88%

Section: Discussionmentioning

confidence: 99%

Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law

2016

Communications in Nonlinear Science and Numerical Simulation

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“…Up to now we have only shown examples of linear Gaussian signals for which the derived relations among C x , C |x| and C s (Eqs. (8), (17) and (19)) must hold. Nevertheless, if we consider nonlinear Gaussian signals, i.e.…”

Section: Example Of a Nonlinear Modelmentioning

confidence: 98%

“…The exponent α quantifies the strength of the correlations present in the time series and is also related to the power spectrum exponent β and the autocorrelation function exponent γ [4,5]. The scaling analysis of the magnitude series, was first introduced to study nonlinearities in heart-beat fluctuations [3] but since then, examples of quantifying nonlinearity using the DFA exponent of the magnitude series can be found in many other fields such as Fluid Dynamics [6], Geophysical [1,7,8] and Economical time series [9]. The scaling exponent of the magnitude fluctuations is easy to compute and is also related to the width of the multifractal spectrum [10,11], another quantity also frequently used to unveil the nonlinear properties of a signal [12].…”

Section: Introductionmentioning

confidence: 99%

Correlations in magnitude series to assess nonlinearities: Application to multifractal models and heartbeat fluctuations

et al. 2017

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The correlation properties of the magnitude of a time series are associated with nonlinear and multifractal properties and have been applied in a great variety of fields. Here we have obtained the analytical expression of the autocorrelation of the magnitude series (C_{|x|}) of a linear Gaussian noise as a function of its autocorrelation (C_{x}). For both, models and natural signals, the deviation of C_{|x|} from its expectation in linear Gaussian noises can be used as an index of nonlinearity that can be applied to relatively short records and does not require the presence of scaling in the time series under study. In a model of artificial Gaussian multifractal signal we use this approach to analyze the relation between nonlinearity and multifractallity and show that the former implies the latter but the reverse is not true. We also apply this approach to analyze experimental data: heart-beat records during rest and moderate exercise. For each individual subject, we observe higher nonlinearities during rest. This behavior is also achieved on average for the analyzed set of 10 semiprofessional soccer players. This result agrees with the fact that other measures of complexity are dramatically reduced during exercise and can shed light on its relationship with the withdrawal of parasympathetic tone and/or the activation of sympathetic activity during physical activity.

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“…Roughly speaking, the first one is responsible for slow (small in magnitude) increases (positive in sign) of the heart rate, while the second is usually associated with fast (large in magnitude) decreases (negative in sign). Other examples of the usefulness of the magnitude and sign analysis are also found in fluid dynamics [7], geological [8,9], geophysical [10,11], and economical time series [12]. …”

Section: Introductionmentioning

confidence: 99%

Magnitude and sign of long-range correlated time series: Decomposition and surrogate signal generation

et al. 2016

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We systematically study the scaling properties of the magnitude and sign of the fluctuations in correlated time series, which is a simple and useful approach to distinguish between systems with different dynamical properties but the same linear correlations. First, we decompose artificial long-range power-law linearly correlated time series into magnitude and sign series derived from the consecutive increments in the original series, and we study their correlation properties. We find analytical expressions for the correlation exponent of the sign series as a function of the exponent of the original series. Such expressions are necessary for modeling surrogate time series with desired scaling properties. Next, we study linear and nonlinear correlation properties of series composed as products of independent magnitude and sign series. These surrogate series can be considered as a zero-order approximation to the analysis of the coupling of magnitude and sign in real data, a problem still open in many fields. We find analytical results for the scaling behavior of the composed series as a function of the correlation exponents of the magnitude and sign series used in the composition, and we determine the ranges of magnitude and sign correlation exponents leading to either single scaling or to crossover behaviors. Finally, we obtain how the linear and nonlinear properties of the composed series depend on the correlation exponents of their magnitude and sign series. Based on this information we propose a method to generate surrogate series with controlled correlation exponent and multifractal spectrum.

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Effects of non-stationarity on the magnitude and sign scaling in the multi-scale vertical velocity increment

Cited by 17 publications

References 42 publications

Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law

Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law

Correlations in magnitude series to assess nonlinearities: Application to multifractal models and heartbeat fluctuations

Magnitude and sign of long-range correlated time series: Decomposition and surrogate signal generation

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