Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the time series, depending on the value of certain scaling parameter. We show that for continuous functions, the proposed continuous DFA also exhibits fractal properties and approximates a power law with scaling exponent one.
@article{arxiv.2203.15940,
title = {Detrended Fluctuation Analysis for Continuous Real Variable Functions},
author = {Luis Gil-Maqueda and Benjamín A. Itzá-Ortiz},
journal= {arXiv preprint arXiv:2203.15940},
year = {2023}
}