The Signum function method for the generation of correlated dichotomic chains

Apostolov, S. S.; Izrailev, F. M.; Makarov, N. M.; Mayzelis, Z. A.; Melnyk, S. S.; Usatenko, O. V.

doi:10.1088/1751-8113/41/17/175101

Cited by 16 publications

(15 citation statements)

References 22 publications

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“…These results are in agreement with Ref. [29], where an analytical relation between C ( ℓ ) and C sign( ℓ ) was found:

C (l) = \sin [\frac{π}{2} C_{sign} (l)]

valid for γ < 1 and C ( ℓ )>0, i.e., 0.5 < α < 1. Taking into account that the correlations will be much smaller than one for large enough ℓ the sine in Eq.…”

Section: Decomposition Of a Time Series: Correlations In The Magnitudsupporting

confidence: 93%

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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“…These results are in agreement with Ref. [29], where an analytical relation between C ( ℓ ) and C sign( ℓ ) was found:

C (l) = \sin [\frac{π}{2} C_{sign} (l)]

valid for γ < 1 and C ( ℓ )>0, i.e., 0.5 < α < 1. Taking into account that the correlations will be much smaller than one for large enough ℓ the sine in Eq.…”

Section: Decomposition Of a Time Series: Correlations In The Magnitudsupporting

confidence: 93%

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

et al. 2016

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“…If the series of increments {x i } is a linear Gaussian noise, Apostolov et al [23] have shown that the autocorrelation of the sign series C s ( ) can be expressed in terms of the autocorrelation C x ( ) by:…”

Section: B Relation With the Autocorrelation Of The Sign Seriesmentioning

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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“…In addition, |x| = |y| = √ 2/π, and σ |x| =σ |y| = 1 − (2/π). Interestingly, both C s and C m are determined exactly by C. For C s , Apostolov et al have shown [32] that…”

Section: =mentioning

confidence: 99%

Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations

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Gómez-Extremera

Carretero-Campos

et al. 2017

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Fluctuation Analysis (FA) and specially Detrended Fluctuation Analysis (DFA) are techniques commonly used to quantify correlations and scaling properties of complex time series such as the observable outputs of great variety of dynamical systems, from Economics to Physiology. Often, such correlated time series are analyzed using the magnitude and sign decomposition, i.e., by using FA or DFA to study separately the sign and the magnitude series obtained from the original signal. This approach allows for distinguishing between systems with the same linear correlations but different dynamical properties. However, here we present analytical and numerical evidence showing that FA and DFA can lead to spurious results when applied to sign and magnitude series obtained from power-law correlated time series of fractional Gaussian noise (fGn) type. Specifically, we show that: (i) the autocorrelation functions of the sign and magnitude series obtained from fGns are always power-laws; However, (ii) when the sign series presents power-law anticorrelations, FA and DFA wrongly interpret the sign series as purely uncorrelated; Similarly, (iii) when analyzing power-law correlated magnitude (or volatility) series, FA and DFA fail to retrieve the real scaling properties, and identify the magnitude series as purely uncorrelated noise; Finally, (iv) using the relationship between FA and DFA and the autocorrelation function of the time series, we explain analytically the reason for the FA and DFA spurious results, which turns out to be an intrinsic property of both techniques when applied to sign and magnitude series.

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The Signum function method for the generation of correlated dichotomic chains

Cited by 16 publications

References 22 publications

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

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

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

Spurious Results of Fluctuation Analysis Techniques in Magnitude and Sign Correlations

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