Wavelet-Tsallis Entropy Detection and Location of Mean Level-Shifts in Long-Memory fGn Signals

Long-memory processes, in particular fractional Gaussian noise processes, have been applied as models for many phenomena occurring in nature. Non-stationarities, such as trends, mean level-shifts, etc., impact the accuracy of long-memory parameter estimators, giving rise to biases and misinterpretations of the phenomena. In this article, a novel methodology for the detection and location of mean level-shifts in stationary long-memory fractional Gaussian noise (fGn) signals is proposed. It is based on a joint application of the wavelet-Tsallis q-entropy as a preprocessing technique and a peak detection methodology. Extensive simulation experiments in synthesized fGn signals with mean level-shifts confirm that the proposed methodology not only detects, but also locates level-shifts with high accuracy. A comparative study against standard techniques of level-shift detection and location shows that the technique based on wavelet-Tsallis q-entropy outperforms the one based on trees and the Bai and Perron procedure, as well.