Assessing Characteristic Scales Using Wavelets
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The variance of these coefficients can be used to decompose the varia...
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ftdatacite:10.48550/arxiv.1007.4169 2023-05-15T15:04:08+02:00 Assessing Characteristic Scales Using Wavelets Keim, Michael J. Percival, Donald B. 2010 https://dx.doi.org/10.48550/arxiv.1007.4169 https://arxiv.org/abs/1007.4169 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Methodology stat.ME FOS Computer and information sciences Preprint Article article CreativeWork 2010 ftdatacite https://doi.org/10.48550/arxiv.1007.4169 2022-04-01T14:38:49Z Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The variance of these coefficients can be used to decompose the variance of the time series across different scales. A practical definition for characteristic scale can be formulated in terms of peaks in plots of the wavelet variance versus scale. This paper presents basic theory for characteristic scales based upon the discrete wavelet transform, proposes a natural estimator for these scales and provides a large sample theory for this estimator that permits the construction of confidence intervals for a true unknown characteristic scale. Computer experiments are presented that demonstrate the efficacy of the large sample theory for finite sample sizes. Examples of characteristic scale estimation are given for global temperature records, coherent structures in river flows, the Madden-Julian oscillation in an atmospheric time series and transects of one type of Arctic sea ice. : 19 pages, 5 figures Report Arctic Sea ice DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Methodology stat.ME FOS Computer and information sciences |
spellingShingle |
Methodology stat.ME FOS Computer and information sciences Keim, Michael J. Percival, Donald B. Assessing Characteristic Scales Using Wavelets |
topic_facet |
Methodology stat.ME FOS Computer and information sciences |
description |
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The variance of these coefficients can be used to decompose the variance of the time series across different scales. A practical definition for characteristic scale can be formulated in terms of peaks in plots of the wavelet variance versus scale. This paper presents basic theory for characteristic scales based upon the discrete wavelet transform, proposes a natural estimator for these scales and provides a large sample theory for this estimator that permits the construction of confidence intervals for a true unknown characteristic scale. Computer experiments are presented that demonstrate the efficacy of the large sample theory for finite sample sizes. Examples of characteristic scale estimation are given for global temperature records, coherent structures in river flows, the Madden-Julian oscillation in an atmospheric time series and transects of one type of Arctic sea ice. : 19 pages, 5 figures |
format |
Report |
author |
Keim, Michael J. Percival, Donald B. |
author_facet |
Keim, Michael J. Percival, Donald B. |
author_sort |
Keim, Michael J. |
title |
Assessing Characteristic Scales Using Wavelets |
title_short |
Assessing Characteristic Scales Using Wavelets |
title_full |
Assessing Characteristic Scales Using Wavelets |
title_fullStr |
Assessing Characteristic Scales Using Wavelets |
title_full_unstemmed |
Assessing Characteristic Scales Using Wavelets |
title_sort |
assessing characteristic scales using wavelets |
publisher |
arXiv |
publishDate |
2010 |
url |
https://dx.doi.org/10.48550/arxiv.1007.4169 https://arxiv.org/abs/1007.4169 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic Sea ice |
genre_facet |
Arctic Sea ice |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1007.4169 |
_version_ |
1766335955981041664 |