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Detrended fluctuation analysis of functional time series

Author

Listed:
  • Hashemi, Maryam
  • Nasirzadeh, Roya
  • Zamani, Atefeh

Abstract

This paper explores long-range dependence in functional time series, where autocorrelations decay hyperbolically rather than exponentially. Traditional methods for detecting such dependence include R/S analysis, Whittle likelihood, and multifractal detrended fluctuation analysis (MFDFA). Building on recent developments in functional time series modeling, we propose a novel extension termed functional MFDFA to analyze multifractal properties of curve-valued data. A randomized variant of the method is also introduced, and its performance is demonstrated through simulation studies and real data applications.

Suggested Citation

  • Hashemi, Maryam & Nasirzadeh, Roya & Zamani, Atefeh, 2026. "Detrended fluctuation analysis of functional time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 692(C).
    • Handle: RePEc:eee:phsmap:v:692:y:2026:i:c:s0378437126002360
    DOI: 10.1016/j.physa.2026.131500
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