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This study evaluates R software methods for detecting fractal properties in psychological data. The performance of these long memory estimators varies with process complexity, necessitating a combined strategy for accurate parameter estimation.

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Area of Science:

  • Cognitive Psychology
  • Social Psychology
  • Biological Psychology
  • Behavioral Science
  • Time Series Analysis

Background:

  • Empirical studies reveal fractal properties in psychological phenomena.
  • Long-range dependencies, or 1/f noise, are identified in psychological and behavioral time series.
  • Self-similar long memory processes characterize these dependencies.

Purpose of the Study:

  • To evaluate estimators of long memory parameters in R for distinguishing fractal processes.
  • To assess the performance of various R packages (fractal, fracdiff) in analyzing psychological time series.
  • To develop a robust strategy for estimating the long memory parameter 'd' in empirical settings.

Main Methods:

  • Time- and frequency-domain analyses were employed.
  • Evaluated R packages: fractal and fracdiff.
  • Specific estimators included PSD (hurstSpec), DFA, FDWhittle, fdSperio, fdGPH, and fracdiff.

Main Results:

  • Estimator performance is highly dependent on the complexity and parameterization of the underlying process.
  • No single method consistently outperformed others across all conditions.
  • Distinguishing between stationary/nonstationary, short/long memory, and different fractal types proved challenging.

Conclusions:

  • A combined strategy for estimating the long memory parameter 'd' is essential due to varying method performance.
  • The developed strategy was demonstrated on an empirical psychological example.
  • Accurate characterization of fractal properties in psychological data requires careful selection and combination of analytical techniques.