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Related Experiment Videos

Evaluating rescaled ranged analysis for time series

J B Bassingthwaighte1, G M Raymond

  • 1Center for Bioengineering, University of Washington, Seattle 98195.

Annals of Biomedical Engineering
|July 1, 1994
PubMed
Summary
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Rescaled range analysis quantifies time series memory and variance. The trend-corrected Hurst exponent (H) method improves accuracy for correlated signals, affirming natural phenomena

Area of Science:

  • Time series analysis
  • Statistical physics
  • Geophysics

Background:

  • Rescaled range (R/S) analysis characterizes time series and 1-D spatial signals.
  • It measures variance and long-term correlation (memory) using statistical self-similarity.
  • The Hurst exponent (H) quantifies fractal properties, where H = 2 - D (fractal dimension).

Purpose of the Study:

  • To evaluate the accuracy, bias, and limitations of rescaled range analysis.
  • To compare standard R/S analysis with a trend-corrected method for estimating the Hurst exponent (H).
  • To affirm Hurst's conclusion on the prevalence of correlated time series in natural phenomena.

Main Methods:

  • Standard R/S analysis measures the ratio of the range of cumulative deviations to the standard deviation over segments of length tau.

Related Experiment Videos

  • Trend-corrected R/S analysis uses the global mean instead of local means for calculating the range.
  • The methods were tested on fractional Brownian signals with known H values.

    • Main Results:

    • Standard R/S analysis yields biased estimates of H (too low for H > 0.72, too high for H < 0.72).
    • The trend-corrected method provides improved H estimates for signals with H >= 0.5 (positive correlations).
    • Rescaled range analysis exhibits poor convergence, requiring ~2,000 data points for 5% accuracy.

    Conclusions:

    • Trend-corrected rescaled range analysis offers more accurate Hurst exponent (H) estimation for correlated time series.
    • Empirical corrections can mitigate bias in H estimates.
    • The study strongly supports Hurst's findings on the non-random, correlated nature of many natural time series.