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Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation

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https://hdl.handle.net/10037/13671
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Date
2017-04-19
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Theodorsen, Audun; Garcia, Odd Erik; Rypdal, Martin Wibe
Abstract
Filtered Poisson processes are often used as reference models for intermittent fluctuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model parameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the model parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.
Description
This is an author-created, un-copyedited version of an article accepted for publication/published in Physica Scripta. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1402-4896/aa694c.
Publisher
IOP Publishing
Citation
Theodorsen, A., Garcia, O.E. & Rypdal, M.W. (2017). Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation. Physica Scripta, 92(5), 1-16. https://doi.org/10.1088/1402-4896/aa694c
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