Characterising the zero-crossing statistics of non-Gaussian stable processes

Slater, Daniel (2019) Characterising the zero-crossing statistics of non-Gaussian stable processes. PhD thesis, University of Nottingham.

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Abstract

Zero-crossing analysis is an old problem, with various attempts to tackle it not yet having led to a universally applicable solution. This is especially true for non-Gaussian stable processes, whose heavy-tails result in problematic statistical properties such as undefined autocorrelation. In this thesis we investigate the need for the coherence (as opposed to the ill-defined autocorrelation) and its applicability in predicting the zero-crossing statistics of non-Gaussian stable processes. This requires us to address the innate issues surrounding estimating the heavy-tailed index for empirical data sets within the stable regime. This includes a review of the ubiquitous Hill estimator, and a comparison of it with a proposed method based on characteristic function analysis by testing them on synthetic and real-world data. The theoretical framework of the thesis is then tested on synthetic data, using a novel method to generate non-Gaussian stable noises. From this it is concluded that coherence offers a means to predict the zero-crossing statistics of stable processes.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Hopcraft, Keith Iain
Sirl, David
Jakeman, Eric
Keywords: Zero-crossing analysis; Non-Gaussian stable processes; Coherence, Non-Gaussian stable noises
Subjects: Q Science > QA Mathematics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 55555
Depositing User: Slater, Daniel
Date Deposited: 19 Jul 2019 12:48
Last Modified: 07 May 2020 11:32
URI: http://eprints.nottingham.ac.uk/id/eprint/55555

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