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Preservation of long range temporal correlations under extreme random dilution

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  • Mirzayof, Dror
  • Ashkenazy, Yosef

Abstract

Many natural time series exhibit long range temporal correlations that may be characterized by power-law scaling exponents. However, in many cases, the time series have uneven time intervals due to, for example, missing data points, noisy data, and outliers. Here we study the effect of randomly missing data points on the power-law scaling exponents of time series that are long range temporally correlated. The Fourier transform and detrended fluctuation analysis (DFA) techniques are used for scaling exponent estimation. We find that even under extreme dilution of more than 50%, the value of the scaling exponent remains almost unaffected. Random dilution is also applied on heart interbeat interval time series. It is found that dilution of 70%–80% of the data points leads to a reduction of only 8% in the scaling exponent; it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90%.

Suggested Citation

  • Mirzayof, Dror & Ashkenazy, Yosef, 2010. "Preservation of long range temporal correlations under extreme random dilution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5573-5580.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5573-5580
    DOI: 10.1016/j.physa.2010.08.035
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    References listed on IDEAS

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    1. Peter Huybers & William Curry, 2006. "Links between annual, Milankovitch and continuum temperature variability," Nature, Nature, vol. 441(7091), pages 329-332, May.
    2. Plamen Ch. Ivanov & Luís A. Nunes Amaral & Ary L. Goldberger & Shlomo Havlin & Michael G. Rosenblum & Zbigniew R. Struzik & H. Eugene Stanley, 1999. "Multifractality in human heartbeat dynamics," Nature, Nature, vol. 399(6735), pages 461-465, June.
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    1. Gilney Figueira Zebende & Florêncio Mendes Oliveira Filho & Juan Alberto Leyva Cruz, 2017. "Auto-correlation in the motor/imaginary human EEG signals: A vision about the FDFA fluctuations," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-13, September.
    2. Filho, F.M. Oliveira & Ribeiro, F.F. & Cruz, J.A. Leyva & de Castro, A.P. Nunes & Zebende, G.F., 2023. "Statistical study of the EEG in motor tasks (real and imaginary)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).

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