Abstract
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.
Highlights
Long-memory phenomena have been observed in many disciplines of science and engineering [1,2,3]
The unbiased estimation of the long-memory parameter in a time series is of crucial importance since, e.g., it could be used as an indicator of the normal or abnormal state in the health of people [11], the likely occurrence of prolonged and increased delays in computer network traffic [12] and as an indicator of a non-stationarity within the fractal signal structure (H > 1)
Signal classification as stationary or non-stationary has been recognized as an important first step in fractal signal analysis [10,14,20,21], and some procedures for classifying a signal as a fractional Gaussian noise or fractional Brownian motion have been proposed [5,10,14,22]
Summary
Long-memory phenomena have been observed in many disciplines of science and engineering [1,2,3]. Long-memory, called, power-law correlations, long-range correlations, long-range dependence, etc., has been observed in human gait [4], heart-rate fluctuations [5], mental activities [6], river flow fluctuations [7], variable-bit-rate (VBR) video traffic [8], economics [9] and in many other physiological time series, such as self-esteem, mood and serial reaction time, among others [10] The result within these contributions is a Hurst parameter H > 1/2, which indicates a power-law decay of autocorrelations at a critical point and a power spectral density (PSD) that diverges at the origin. This paper proposes a technique for mean level-shift detection and location in stationary fGn signals of parameter H This technique is based on a joint application of the wavelet-Tsallis q-entropy and a standard peak detection and location methodology.
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