Exploring Stochastic Time Series Structure Through Wavelet Entropy

The article is dedicated to investigating the application of discrete wavelet transform (DWT) to detect structural changes in non-stationary stochastic time series. The computational experiment shows the effectiveness of applying wavelet entropy and relative wavelet entropy to this analysis. The paper focuses on adaptive estimation of the relative wavelet entropy based on underlying time series or their previous segment. The latter approach is applicable if no prior information about the structure of the analyzed series is available, while the former is effective in identifying differences from a known process. Combining these two methods enables accurate tracking of time series segments with significantly different behavioural characteristics. The proposed approaches are tested on synthetic signals and applied to analyzing real-world time series of encephalograms. The experiment demonstrates that the adaptive estimation of wavelet entropy and relative entropy of EEG signals allows for determining the reaction time to external stimuli that can be useful in diagnosing neurological diseases.