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Spectral analysis of high-dimensional time series
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Fiecas, Mark, Leng, Chenlei, Liu, Weidong and Yu, Yi (2019) Spectral analysis of high-dimensional time series. Electronic Journal of Statistics, 13 (2). pp. 4079-4101. doi:10.1214/19-EJS1621
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Official URL: http://dx.doi.org/10.1214/19-EJS1621
Abstract
A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length, regularisation based methods can overcome the curse of dimensionality, but the existing ones lack theoretical justification. This paper develops the first non-asymptotic result for characterising the difference between the sample and population versions of the spectral density matrix, allowing one to justify a range of high-dimensional models for analysing time series. As a concrete example, we apply this result to establish the convergence of the smoothed periodogram estimators and sparse estimators of the inverse of spectral density matrices, namely precision matrices. These results, novel in the frequency domain time series analysis, are corroborated by simulations and an analysis of the Google Flu Trends data.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Time-series analysis, Spectral energy distribution, Density matrices, Multivariate analysis | |||||||||
| Journal or Publication Title: | Electronic Journal of Statistics | |||||||||
| Publisher: | Institute of Mathematical Statistics | |||||||||
| ISSN: | 1935-7524 | |||||||||
| Official Date: | 2019 | |||||||||
| Dates: |
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| Volume: | 13 | |||||||||
| Number: | 2 | |||||||||
| Page Range: | pp. 4079-4101 | |||||||||
| DOI: | 10.1214/19-EJS1621 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| RIOXX Funder/Project Grant: |
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