Visualization and inference based on wavelet coefficients, SiZer and SiNos
Fred Godtliebsen, Murad S. Taqqu, Cheolwoo Park, J. S. Marron, Stilian Stoev · Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2021
SiZer (SIgnificant ZERo crossing of the derivatives) and SiNos (SIgnificant NOnStationarities) are scale-space based visualization tools for statistical inference. They are used to discover meaningful structure in data through exploratory analysis involving statistical smoothing techniques. Wavelet methods have been successfully used to analyze various types of time series. In this paper, we propose a new time series analysis approach, which combines the wavelet analysis with the visualization tools SiZer and SiNos. We use certain functions of wavelet coefficients at different scales as inputs, and then apply SiZer or SiNos to highlight potential non-stationarities. We show that this new methodology can reveal hidden local non-stationary behavior of time series, that are otherwise difficult to detect.