Characterising the zero-crossing statistics of non-Gaussian stable processes
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 t...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2019
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| Online Access: | https://eprints.nottingham.ac.uk/55555/ |
| _version_ | 1848799182744190976 |
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| author | Slater, Daniel |
| author_facet | Slater, Daniel |
| author_sort | Slater, Daniel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:31:36Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-55555 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:31:36Z |
| publishDate | 2019 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-555552025-02-28T14:18:14Z https://eprints.nottingham.ac.uk/55555/ Characterising the zero-crossing statistics of non-Gaussian stable processes Slater, Daniel 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. 2019-07-18 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/55555/1/D%20Slater%20-%20Characterising%20the%20zero-crossing%20statistics%20of%20non-Gaussian%20stable%20processes.pdf Slater, Daniel (2019) Characterising the zero-crossing statistics of non-Gaussian stable processes. PhD thesis, University of Nottingham. Zero-crossing analysis; Non-Gaussian stable processes; Coherence Non-Gaussian stable noises |
| spellingShingle | Zero-crossing analysis; Non-Gaussian stable processes; Coherence Non-Gaussian stable noises Slater, Daniel Characterising the zero-crossing statistics of non-Gaussian stable processes |
| title | Characterising the zero-crossing statistics of non-Gaussian stable processes |
| title_full | Characterising the zero-crossing statistics of non-Gaussian stable processes |
| title_fullStr | Characterising the zero-crossing statistics of non-Gaussian stable processes |
| title_full_unstemmed | Characterising the zero-crossing statistics of non-Gaussian stable processes |
| title_short | Characterising the zero-crossing statistics of non-Gaussian stable processes |
| title_sort | characterising the zero-crossing statistics of non-gaussian stable processes |
| topic | Zero-crossing analysis; Non-Gaussian stable processes; Coherence Non-Gaussian stable noises |
| url | https://eprints.nottingham.ac.uk/55555/ |