A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series
This paper proposes a frequency domain approach to test the hypothesis that a complex-valued vector time series is proper, i.e., for testing whether the vector time series is uncorrelated with its complex conjugate. If the hypothesis is rejected, frequency bands causing the rejection will be identif...
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ftdatacite:10.48550/arxiv.1605.05910 2023-05-15T17:06:11+02:00 A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series Chandna, Swati Walden, Andrew T. 2016 https://dx.doi.org/10.48550/arxiv.1605.05910 https://arxiv.org/abs/1605.05910 unknown arXiv https://dx.doi.org/10.1109/tsp.2016.2639459 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Methodology stat.ME Applications stat.AP FOS Computer and information sciences article-journal Article ScholarlyArticle Text 2016 ftdatacite https://doi.org/10.48550/arxiv.1605.05910 https://doi.org/10.1109/tsp.2016.2639459 2022-04-01T11:34:15Z This paper proposes a frequency domain approach to test the hypothesis that a complex-valued vector time series is proper, i.e., for testing whether the vector time series is uncorrelated with its complex conjugate. If the hypothesis is rejected, frequency bands causing the rejection will be identified and might usefully be related to known properties of the physical processes. The test needs the associated spectral matrix which can be estimated by multitaper methods using, say, $K$ tapers. Standard asymptotic distributions for the test statistic are of no use since they would require $K \rightarrow \infty,$ but, as $K$ increases so does resolution bandwidth which causes spectral blurring. In many analyses $K$ is necessarily kept small, and hence our efforts are directed at practical and accurate methodology for hypothesis testing for small $K.$ Our generalized likelihood ratio statistic combined with exact cumulant matching gives very accurate rejection percentages and outperforms other methods. We also prove that the statistic on which the test is based is comprised of canonical coherencies arising from our complex-valued vector time series.Our methodology is demonstrated on ocean current data collected at different depths in the Labrador Sea. Overall this work extends results on propriety testing for complex-valued vectors to the complex-valued vector time series setting. : 13 pages, 3 figures. Methodology (stat.ME), Applications (stat.AP) Text Labrador Sea DataCite Metadata Store (German National Library of Science and Technology) |
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Methodology stat.ME Applications stat.AP FOS Computer and information sciences |
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Methodology stat.ME Applications stat.AP FOS Computer and information sciences Chandna, Swati Walden, Andrew T. A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series |
topic_facet |
Methodology stat.ME Applications stat.AP FOS Computer and information sciences |
description |
This paper proposes a frequency domain approach to test the hypothesis that a complex-valued vector time series is proper, i.e., for testing whether the vector time series is uncorrelated with its complex conjugate. If the hypothesis is rejected, frequency bands causing the rejection will be identified and might usefully be related to known properties of the physical processes. The test needs the associated spectral matrix which can be estimated by multitaper methods using, say, $K$ tapers. Standard asymptotic distributions for the test statistic are of no use since they would require $K \rightarrow \infty,$ but, as $K$ increases so does resolution bandwidth which causes spectral blurring. In many analyses $K$ is necessarily kept small, and hence our efforts are directed at practical and accurate methodology for hypothesis testing for small $K.$ Our generalized likelihood ratio statistic combined with exact cumulant matching gives very accurate rejection percentages and outperforms other methods. We also prove that the statistic on which the test is based is comprised of canonical coherencies arising from our complex-valued vector time series.Our methodology is demonstrated on ocean current data collected at different depths in the Labrador Sea. Overall this work extends results on propriety testing for complex-valued vectors to the complex-valued vector time series setting. : 13 pages, 3 figures. Methodology (stat.ME), Applications (stat.AP) |
format |
Text |
author |
Chandna, Swati Walden, Andrew T. |
author_facet |
Chandna, Swati Walden, Andrew T. |
author_sort |
Chandna, Swati |
title |
A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series |
title_short |
A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series |
title_full |
A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series |
title_fullStr |
A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series |
title_full_unstemmed |
A Frequency Domain Test for Propriety of Complex-Valued Vector Time Series |
title_sort |
frequency domain test for propriety of complex-valued vector time series |
publisher |
arXiv |
publishDate |
2016 |
url |
https://dx.doi.org/10.48550/arxiv.1605.05910 https://arxiv.org/abs/1605.05910 |
genre |
Labrador Sea |
genre_facet |
Labrador Sea |
op_relation |
https://dx.doi.org/10.1109/tsp.2016.2639459 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1605.05910 https://doi.org/10.1109/tsp.2016.2639459 |
_version_ |
1766061195257708544 |