Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques

Xu, Limei; Ivanov, Plamen Ch.; Hu, Kun; Chen, Zhi; Carbone, Anna Filomena; Stanley, H. Eugene

doi:10.1103/physreve.71.051101

Cited by 274 publications

(196 citation statements)

References 62 publications

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“…Compared with traditional correlation analyses such as power spectral analysis and Hurst analysis, the DFA can accurately quantify correlations in signals that may be masked by underlying nonstationarities or trends (Hu et al, 2001;Chen et al, 2002;Xu et al, 2005). We used DFA to quantify the detrended fluctuations F(n) of activity at different time scales n. For each chosen time scale n, the DFA method involves the following steps (Peng et al, 1994): i) integrating the time series; ii) dividing the integrated time series into non-overlapped bins of equal size n (the chosen time scale); iii) in each bin, fitting the integrated time series with a second order polynomial function, which defines 'local' trends assumed to be the result of external influences.…”

Section: (I) Correlation Analysismentioning

confidence: 99%

The suprachiasmatic nucleus functions beyond circadian rhythm generation

et al. 2007

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We recently discovered that human activity possesses a complex temporal organization characterized by scale-invariant/self-similar fluctuations from seconds to ~4 hour-statistical properties of fluctuations remain the same at different time scales. Here, we show that scale-invariant activity patterns are essentially identical in humans and rats, and exist for up to ~24 hour: six-times longer than previously documented. Theoretically, such scale-invariant patterns can be produced by a neural network of interacting control nodes-system components with feedback loops-operating at different time scales. However such control nodes have not yet been identified in any neurophysiological model of scale invariance/self-similarity in mammals. Here we demonstrate that the endogenous circadian pacemaker (suprachiasmastic nucleus; SCN), known to modulate locomotor activity with a periodicity of ~24 hour, also acts as a major neural control node responsible for the generation of scale-invariant locomotor patterns over a broad range of time scales from minutes to at least 24 hour (rather than solely at ~24 hour). Remarkably, we found that SCN lesion in rats completely abolished the scale-invariant locomotor pattern between 4 and 24 hour and significantly altered the patterns at time scales <4 hour. Identification of the control nodes of a neural network responsible for scale invariance is the critical first step in understanding the neurophysiological origin of scale invariance/self-similarity. KeywordsActivity; Scale-invariance; Suprachiasmatic nucleus lesion; Human; Rat; Network The suprachiasmastic nucleus (SCN) in mammals generates self-sustained oscillations that orchestrate a wide range of neurophysiologic functions-from cellular processes to overt behaviors-with a time period of ~24 hour (Weaver, 1998). One of the fundamental processes influenced by the SCN is motor activity, which displays clear ~24 hour rhythms even under

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Section: (I) Correlation Analysismentioning

confidence: 99%

The suprachiasmatic nucleus functions beyond circadian rhythm generation

et al. 2007

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“…(2)) at the boundaries of the segments, since the fitting polynomials in neighboring segments are not related. As a simple way to avoid these jumps the central moving average (CMA) method was suggested recently [19] (see also [20], where this method is compared with the backward moving average technique). In CMA, Eq.…”

Section: Central Moving Average (Cma) Analysismentioning

confidence: 99%

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

Bartsch¹,

Plotnik²,

Kantelhardt³

et al. 2007

Physica A: Statistical Mechanics and its Applications

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We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.

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“…For recent comparative studies not focused on detrending methods, see [14,17,18]. For studies comparing DFA and BMA, see [46,47]; note that [47] also discusses CMA. For studies comparing methods for detrending multifractal analysis (multifractal DFA (MF-DFA) and wavelet transform modulus maxima (WTMM) method), see [5,24,48].…”

Section: Introductionmentioning

confidence: 99%

Comparison of detrending methods for fluctuation analysis

Bashan

Bartsch

Kantelhardt

et al. 2008

Physica A: Statistical Mechanics and its Applications

286

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We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA is performing equivalently as DFA in long data with weak trends and slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect the different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.

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Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques

Cited by 274 publications

References 62 publications

The suprachiasmatic nucleus functions beyond circadian rhythm generation

The suprachiasmatic nucleus functions beyond circadian rhythm generation

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

Comparison of detrending methods for fluctuation analysis

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