Zhi Chen

TL;DR: It is shown how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.

TL;DR: In this article, the effects of three types of non-stationarities often encountered in real data were studied. And the authors compared the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types and showed how the characteristics of these crossovers depend on the fraction and size of the parts cut out from the signal, the concentration of spikes and their amplitudes.

TL;DR: It is found that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and it is shown how to develop strategies for preprocessing "raw" data prior to analysis, which will minimize the effects of non stationarities on the scaling properties of the data.

TL;DR: It is found that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter, and the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) is investigated.

TL;DR: This work investigates how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals.