  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.
