Visualization and inference based on wavelet coefficients, SiZer and SiNos

Authors:
Cheolwoo Park;Fred Godtliebsen;Murad Taqqu;Stilian Stoev;J. S. Marron
Affiliations:
Department of Statistics, University of Georgia, Athens, GA 30602-1952, USA;Department of Mathematics and Statistics, University of Tromsø, N-9037 Tromsø, Norway;Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA;Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1107, USA;Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260, USA
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

SiZer (SIgnificant ZERo crossing of the derivatives) and SiNos (SIgnificant NOn-Stationarities) 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.