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Article overview
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Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis | | Qianli D.Y. Ma
; Ronny P. Bartsch
; Pedro Bernaola-Galván
; Mitsuru Yoneyama
; Plamen Ch. Ivanov
; | | Date: |
20 Jan 2010 | | Abstract: | We investigate how extreme loss of data affects the scaling behavior of
long-range power-law correlated and anti-correlated signals applying the DFA
method. We introduce a segmentation approach to generate surrogate signals by
randomly removing data segments from stationary signals with different types of
correlations. These surrogate signals are characterized by: (i) the DFA scaling
exponent $alpha$ of the original correlated signal, (ii) the percentage $p$ of
the data removed, (iii) the average length $mu$ of the removed (or remaining)
data segments, and (iv) the functional form of the distribution of the length
of the removed (or remaining) data segments. We find that the {it global}
scaling exponent of positively correlated signals remains practically unchanged
even for extreme data loss of up to 90%. In contrast, the global scaling of
anti-correlated signals changes to uncorrelated behavior even when a very small
fraction of the data is lost. These observations are confirmed on the examples
of human gait and commodity price fluctuations. We systematically study the
{it local} scaling behavior of signals with missing data to reveal deviations
across scales. We find that for anti-correlated signals even 10% of data loss
leads to deviations in the local scaling at large scales from the original
anti-correlated towards uncorrelated behavior. In contrast, positively
correlated signals show no observable changes in the local scaling for up to
65% of data loss, while for larger percentage, the local scaling shows
overestimated regions (with higher local exponent) at small scales, followed by
underestimated regions (with lower local exponent) at large scales. Finally, we
investigate how the scaling is affected by the statistics of the remaining data
segments in comparison to the removed segments. | | Source: | arXiv, 1001.3641 | | Services: | Forum | Review | PDF | Favorites | |
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