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Detecting switching points using asymmetric detrended fluctuation analysis

Author

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  • Rivera-Castro, Miguel A.
  • Miranda, José G.V.
  • Cajueiro, Daniel O.
  • Andrade, Roberto F.S.

Abstract

This work uses the concept of Asymmetric Detrended Fluctuation Analysis (A-DFA) to investigate and characterize the occurrence of trend switching in financial series. A-DFA introduces two new roughness exponents, H+ and H−, which differ from the usual one H by separately taking into account contributions to the fluctuations according to whether the local trend is, respectively, upward or downward. The developed methodology requires the evaluation of local values of H(t),H+(t), and H−(t), by restricting the size of the largest window around the value t. We show that H+(t) and H−(t) behave differently in the neighborhoods of switching points (SPs) where trends change sign. Properly taken differences between shifted local values of H(t),H+(t), and H−(t) allow to identify and characterize SP’s. Tests with Weiertrasse functions, isolated peaks, and actual financial series are presented, supporting the validity of the proposed method.

Suggested Citation

  • Rivera-Castro, Miguel A. & Miranda, José G.V. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "Detecting switching points using asymmetric detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 170-179.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:170-179
    DOI: 10.1016/j.physa.2011.07.009
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