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.
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February 2020
Research Article|
February 11 2020
Bispectral unfolding of the skewness of correlated additive and multiplicative noise processes
Adam H. Monahan
Adam H. Monahan
a)
School of Earth and Ocean Sciences, University of Victoria
, PO Box 1700 STN CSC, Victoria, British Columbia V8W2Y2, Canada
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Author to whom correspondence should be addressed: [email protected]
Chaos 30, 023126 (2020)
Article history
Received:
August 26 2019
Accepted:
January 14 2020
Citation
Adam H. Monahan; Bispectral unfolding of the skewness of correlated additive and multiplicative noise processes. Chaos 1 February 2020; 30 (2): 023126. https://doi.org/10.1063/1.5125787
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