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2019 Spectral analysis of high-dimensional time series
Mark Fiecas, Chenlei Leng, Weidong Liu, Yi Yu
Electron. J. Statist. 13(2): 4079-4101 (2019). DOI: 10.1214/19-EJS1621


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.


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Mark Fiecas. Chenlei Leng. Weidong Liu. Yi Yu. "Spectral analysis of high-dimensional time series." Electron. J. Statist. 13 (2) 4079 - 4101, 2019.


Received: 1 November 2018; Published: 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07116197
MathSciNet: MR4017528
Digital Object Identifier: 10.1214/19-EJS1621


Vol.13 • No. 2 • 2019
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