A hybrid detrending method for fractional Gaussian noise

Determining trend and implementing detrending operations are important steps in data analysis. Yet there is neither precise definition of “trend” nor any logical algorithm for extracting it. In this paper, we propose a Hybrid Detrending Method (HDM) which is based on the Empirical Mode Decomposition (EMD) and the Detrended Fluctuation Analysis (DFA). Our method can remove the polynomial and sinusoidal trends from the fractional Gaussian noise (fGn) background. We illustrate the method by selected examples from artificial time series and climate data. In comparison with existing frequency domain based detrending methods, our method is a posteriori, the trend defined by our method is only derived from the data. Further, our method also preserves the scaling behavior of the original signals.