G-Filtering Nonstationary Time Series

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series,...

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Bibliographic Details
Main Authors: Mengyuan Xu, Krista B. Cohlmia, Wayne A. Woodward, Henry L. Gray
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2012/738636
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Summary:The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.
ISSN:1687-952X
1687-9538