Publication Date:
2022-05-26
Description:
Author Posting. © The Authors, 2019. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 218(3), (2019): 2165-2178, doi: 10.1093/gji/ggz280.
Description:
A multitaper estimator is proposed that accommodates time-series containing gaps without using any form of interpolation. In contrast with prior missing-data multitaper estimators that force standard Slepian sequences to be zero at gaps, the proposed missing-data Slepian sequences are defined only where data are present. The missing-data Slepian sequences are frequency independent, as are the eigenvalues that define the energy concentration within the resolution bandwidth, when the process bandwidth is [−1/2,1/2) for unit sampling and the sampling scheme comprises integer multiples of unity. As a consequence, one need only compute the ensuing missing-data Slepian sequences for a given sampling scheme once, and then the spectrum at an arbitrary set of frequencies can be computed using them. It is also shown that the resulting missing-data multitaper estimator can incorporate all of the optimality features (i.e. adaptive-weighting, F-test and reshaping) of the standard multitaper estimator, and can be applied to bivariate or multivariate situations in similar ways. Performance of the missing-data multitaper estimator is illustrated using length of day, seafloor pressure and Nile River low stand time-series.
Description:
The length of day utilized in Section 3 are available from http://hpiers.obspm.fr. The pressure data used in Section 4 are available from https://doi.org/10.1029/2018JC014586. A Matlab function MDmwps.m to compute missing-data power spectra is available from the Mathworks file exchange website. The author thanks Jeff Park and editor F.J. Simons for thorough reviews. This work was supported by an Internal Research and Development award at WHOI, and by the Walter A. and Hope Noyes Smith Chair for Excellence in Oceanography.
Keywords:
Fourier analysis
;
Numerical approximations and analysis
;
Statistical methods
;
Time-series analysis
Repository Name:
Woods Hole Open Access Server
Type:
Article
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