Data-driven shrinkage of the spectral density matrix of a high-dimensional time series

Mark Fiecas, Rainer von Sachs

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Time series data obtained from neurophysiological signals is often high-dimensional and the length of the time series is often short relative to the number of dimensions. Thus, it is difficult or sometimes impossible to compute statistics that are based on the spectral density matrix because estimates of these matrices are often numerically unstable. In this work, we discuss the importance of regularization for spectral analysis of high dimensional time series and propose shrinkage estimation for estimating high dimensional spectral density matrices. We use and develop the multivariate Time-frequency Toggle (TFT) bootstrap procedure for multivariate time series to estimate the shrinkage parameters, and show that the multivariate TFT bootstrap is theoretically valid. We show via simulations and an fMRI data set that failure to regularize the estimates of the spectral density matrix can yield unstable statistics, and that this can be alleviated by shrinkage estimation.

Original languageEnglish (US)
Pages (from-to)2975-3003
Number of pages29
JournalElectronic Journal of Statistics
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2014, Institute of Mathematical Statistics. All rights reserved.


  • Bootstrap
  • High-dimensional time series
  • Shrinkage estimation
  • Spectral analysis


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