Detrended fluctuation analysis as a regression framework: Estimating dependence at different scales

TL;DR

This paper introduces a novel regression framework based on detrended fluctuation analysis that estimates relationships between variables at multiple scales, effectively handling non-stationarity and power-law correlations.

Contribution

It combines detrended fluctuation analysis with regression to estimate scale-dependent effects, improving over traditional methods especially in non-stationary contexts.

Findings

Relationship between variables varies across scales in most cases.

The method outperforms standard least squares in non-stationary data.

Applicable across physics, finance, environmental science, and epidemiology.

Abstract

We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential non-stationarity and power-law correlations. The former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives. The latter ones make the method a significant improvement over the standard least squares estimation. Theoretical claims are supported by Monte Carlo simulations. The method is then applied on selected examples from physics, finance, environmental science and epidemiology. For most of the studied cases, the relationship between variables of interest varies strongly across scales.