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Effect of coarse-graining on detrended fluctuation analysis

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  • Nagarajan, Radhakrishnan

Abstract

Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps the continuous process into digital data. The resulting digital data is discretized in amplitude and time, and shall be referred to as coarse-grained realization in the present study. Since coarse-graining precedes scaling exponent analysis, it is important to understand its effects on scaling exponent estimators such as DFA. In this brief communication, k-means clustering is used to generate coarse-grained realizations of data sets with different correlation properties, namely: anti-correlated noise, long-range correlated noise and uncorrelated noise. It is shown that the coarse-graining can significantly affect the scaling exponent estimates. It is also shown that scaling exponent can be reliably estimated even at low levels of coarse-graining and the number of the clusters required varies across the data sets with different correlation properties.

Suggested Citation

  • Nagarajan, Radhakrishnan, 2006. "Effect of coarse-graining on detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 226-236.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:226-236
    DOI: 10.1016/j.physa.2005.08.029
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    1. Ashkenazy, Yosef & Havlin, Shlomo & Ivanov, Plamen Ch. & Peng, Chung-K. & Schulte-Frohlinde, Verena & Stanley, H.Eugene, 2003. "Magnitude and sign scaling in power-law correlated time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 19-41.
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    Cited by:

    1. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    2. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.

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