G-Filtering Nonstationary Time Series

Abstract EN

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.