Detrended Fluctuation Analysis for Continuous Real Variable Functions

TL;DR

This paper extends Detrended Fluctuation Analysis (DFA) to continuous real variable functions, demonstrating its ability to predict long-term auto-correlation and exhibit fractal properties with a power-law scaling.

Contribution

It introduces a continuous version of DFA for functions, revealing its fractal nature and scaling behavior, which was previously limited to discrete time series.

Findings

DFA for continuous functions accurately predicts long-term auto-correlation.

The continuous DFA exhibits fractal properties and follows a power-law with scaling exponent one.

The method provides a new tool for analyzing continuous data with fractal characteristics.

Abstract

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.