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

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.

10 pages, 6 figures

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• Fractal approach towards power-law coherency to measure cross-correlations between time series
• Power-law cross-correlations estimation under heavy tails
• A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities