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    A frequency domain test for propriety of complex-valued vector time series

    Chandna, Swati and Walden, A. (2016) A frequency domain test for propriety of complex-valued vector time series. IEEE Transactions on Signal Processing 65 (6), pp. 1425-1436. ISSN 1053-587X.

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    This paper proposes a frequency domain approach to test the hypothesis that a stationary complexvalued 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 → ∞, 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. 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. Frequency specific tests are combined using multiple hypothesis testing to give an overall test. 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.


    Item Type: Article
    Additional Information: (c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
    Keyword(s) / Subject(s): Time series, complex-valued signal processing, propriety, circularity, oceanography
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Swati Chandna
    Date Deposited: 10 Jan 2018 14:29
    Last Modified: 12 Jun 2021 08:45


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