G-filtering nonstationary time series. (English) Zbl 1233.62169

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. 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.


62M20 Inference from stochastic processes and prediction
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C60 Computational problems in statistics (MSC2010)


Full Text: DOI


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