A Statistical Analysis of Morse Wavelet Coherence
Wavelet coherence computed from two time series has been widely applied in hypothesis testing situations, but has proven resistant to analytic study, with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationar...
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| Veröffentlicht in: | IEEE transactions on signal processing 2010-03, Vol.58 (3), p.980-989 |
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| container_end_page | 989 |
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| container_title | IEEE transactions on signal processing |
| container_volume | 58 |
| creator | Cohen, E.A.K. Walden, A.T. |
| description | Wavelet coherence computed from two time series has been widely applied in hypothesis testing situations, but has proven resistant to analytic study, with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. If estimated using multiple orthogonal Morse wavelets, wavelet coherence is in fact amenable to statistical study. Since the wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is, for large samples, appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent. Theoretical results are illustrated and verified via simulations. |
| doi_str_mv | 10.1109/TSP.2009.2033645 |
| format | Article |
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As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. If estimated using multiple orthogonal Morse wavelets, wavelet coherence is in fact amenable to statistical study. Since the wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is, for large samples, appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent. 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As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. If estimated using multiple orthogonal Morse wavelets, wavelet coherence is in fact amenable to statistical study. Since the wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is, for large samples, appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent. Theoretical results are illustrated and verified via simulations.</description><subject>Analytical models</subject><subject>Applied sciences</subject><subject>Coherence</subject><subject>Computational modeling</subject><subject>Computer simulation</subject><subject>Discrete wavelet transforms</subject><subject>Equivalence</subject><subject>Exact sciences and technology</subject><subject>Gaussian distribution</subject><subject>Goodman distribution</subject><subject>Information, signal and communications theory</subject><subject>Mathematical analysis</subject><subject>Miscellaneous</subject><subject>Morse wavelets</subject><subject>Null hypothesis</subject><subject>Signal processing</subject><subject>Statistical analysis</subject><subject>Telecommunications and information theory</subject><subject>Testing</subject><subject>Time series</subject><subject>Time series analysis</subject><subject>Wavelet</subject><subject>Wavelet analysis</subject><subject>wavelet coherence</subject><subject>Wavelet domain</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkE1LAzEQhoMoWKt3wcsiiKetk8_dHEvxCyoKregtpNkJbtl2NdkK_femtvTgxUsmzDwz8D6EnFMYUAr6Zjp5GTAAnR7OlZAHpEe1oDmIQh2mP0iey7J4PyYnMc4BqBBa9QgdZpPOdnXsamebbLi0zTrWMWt99tSGiNmb_cYGu2zUfmDApcNTcuRtE_FsV_vk9e52OnrIx8_3j6PhOHei4F1uKbOlkuAdd5xbWrGZoC71LOVUesYoA-uqyhUzr0srJQf02pWYioKK8T653t79DO3XCmNnFnV02DR2ie0qmrKQwLRKaf8jC8ELBfBLXv4h5-0qpMzR6GSrVIxDgmALudDGGNCbz1AvbFgbCmbj2iTXZuPa7FynlavdXRuTRh_s0tVxv8eYSHEFTdzFlqsRcT-WrASepj-MvIUC</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>Cohen, E.A.K.</creator><creator>Walden, A.T.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Analytical models Applied sciences Coherence Computational modeling Computer simulation Discrete wavelet transforms Equivalence Exact sciences and technology Gaussian distribution Goodman distribution Information, signal and communications theory Mathematical analysis Miscellaneous Morse wavelets Null hypothesis Signal processing Statistical analysis Telecommunications and information theory Testing Time series Time series analysis Wavelet Wavelet analysis wavelet coherence Wavelet domain |
| title | A Statistical Analysis of Morse Wavelet Coherence |
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