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Bispectral unfolding of the skewness of correlated additive and multiplicative noise processes. (English) Zbl 1440.62340
Summary: 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.
##### 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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