Title: Probabilistic properties of detrended fluctuation analysis for Gaussian processes
Authors: Grzegorz Sikora - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: The detrended fluctuation analysis is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown as one of the best performing detrending methods, its probabilistic foundations are still unclear. We study the probabilistic properties of DFA for Gaussian processes. The main attention is paid to the distribution of the squared error sum of the detrended process. This allows us to find the expected value and the variance of the squared fluctuation function of DFA for a Gaussian process of a general form. The results can serve as a starting point for analyzing the statistical properties of the DFA-based estimators for the fluctuation function and long-memory parameters. The obtained theoretical results are supported by numerical simulations.