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**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.

### MSC:

62M20 | Inference from stochastic processes and prediction |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

65C60 | Computational problems in statistics (MSC2010) |

### Software:

GW-WINKS
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\textit{M. Xu} et al., J. Probab. Stat. 2012, Article ID 738636, 15 p. (2012; Zbl 1233.62169)

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### References:

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