title: 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 nonstationarity 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.
authors.affiliation: Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodarenskou vezi 4, Prague, CZ-182 08, Czech Republic, Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Opletalova 26, Prague, CZ-110 00, Czech Republic, and Warwick Business School, University of Warwick, Coventry, West Midlands, CV4 7AL, United Kingdom.
authors.forename: Ladislav
authors.initials: L
authors.lastname: Kristoufek