Spectral analysis of high-dimensional time series

Mark Fiecas, Chenlei Leng, Weidong Liu, Yi Yu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4079-4101
Number of pages23
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2019

Bibliographical note

Funding Information:
∗We are very grateful to the Editor and two referees for their constructive comments. †Leng was supported by a Turing fellowship from the Alan Turing Institute under the EPSRC grant EP/N510129/1

Publisher Copyright:
© 2019, Institute of Mathematical Statistics. All rights reserved.


  • Frequency domain time series
  • Functional dependency
  • High dimension
  • Smoothed periodogram
  • Sparse precision matrix estimation


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