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Detecting multifractality and exposing distributions of local fluctuations: Detrended fluctuation analysis with descriptive statistics pooling

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  • Telli, Şahin
  • Chen, Hongzhuan
  • Zhao, Xufeng

Abstract

In this article, DFA is expanded to detect multifractality in time series and to reveal the distributions of fluctuations. The method, Detrended Fluctuation Analysis with Descriptive Statistics Pooling (DFA-DSP), is introduced, tested and studied. Following the introduction of the method, robustness tests are conducted on computer generated data sets and compared with MF-DFA results. The MF-DFA findings for q=2 are identical to the DFA-DSP findings for a certain parameter value. Tests showed that the proposed method can be used to detect and measure multifractality in the time series. Given real data, similar results to those reported in the literature using MF-DFA were obtained. Furthermore, using min and max as pooling functions, the suggested method imitates the MF-DFA results for small and large fluctuations.

Suggested Citation

  • Telli, Şahin & Chen, Hongzhuan & Zhao, Xufeng, 2022. "Detecting multifractality and exposing distributions of local fluctuations: Detrended fluctuation analysis with descriptive statistics pooling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010328
    DOI: 10.1016/j.chaos.2021.111678
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    References listed on IDEAS

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