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G-Filtering Nonstationary Time Series

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  • Mengyuan Xu
  • Krista B. Cohlmia
  • Wayne A. Woodward
  • Henry L. Gray

Abstract

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.

Suggested Citation

  • Mengyuan Xu & Krista B. Cohlmia & Wayne A. Woodward & Henry L. Gray, 2012. "G-Filtering Nonstationary Time Series," Journal of Probability and Statistics, Hindawi, vol. 2012, pages 1-15, March.
    • Handle: RePEc:hin:jnljps:738636
    DOI: 10.1155/2012/738636
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