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Title: Characterising the zero-crossing statistics of non-Gaussian stable processes
Author: Slater, Daniel
ISNI:       0000 0004 7965 6458
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2019
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics