Bispectral unfolding of the skewness of correlated additive and multiplicative noise processes.

*(English)*Zbl 1440.62340Summary: Correlated additive and multiplicative (CAM) noise processes are well-established as general “null hypothesis” models of non-Gaussian variability in atmospheric and oceanic quantities. In this study, analytic expressions for the bispectral density (which partitions the third statistical moment into triad frequency interactions in a manner analogous to the partitioning of variance by the spectral density) are developed for discrete and continuous-time CAM processes. It is then demonstrated that under lowpass filtering, while the absolute skewness of a discrete-time CAM process may increase or decrease with decreasing cutoff frequency, the absolute skewness of continuous-time CAM processes decreases monotonically. This second result provides a test to assess the degree to which an observed time series is consistent with continuous-time CAM dynamics.

©2020 American Institute of Physics

©2020 American Institute of Physics

##### MSC:

62M15 | Inference from stochastic processes and spectral analysis |

62H20 | Measures of association (correlation, canonical correlation, etc.) |

34F05 | Ordinary differential equations and systems with randomness |

37M10 | Time series analysis of dynamical systems |

62P35 | Applications of statistics to physics |

86A32 | Geostatistics |

85A20 | Planetary atmospheres |

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##### References:

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