Shrinkage estimation for multivariate time series

Yan Liu*, Yoshiyuki Tanida, Masanobu Taniguchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper deals with shrinkage estimators for the mean of p-dimensional Gaussian stationary processes. The shrinkage estimators are expressed by a shrinkage function, including the sample mean and the James–Stein estimator as special cases. We evaluate the mean squared error of such shrinkage estimators from the true mean of a p-dimensional Gaussian vector stationary process with p≥ 3. A sufficient condition for shrinkage estimators improving the mean squared error upon the sample mean is given in terms of the shrinkage function and the spectral density matrix. In addition, a shrinkage estimator, providing the most significant improvement to the sample mean, is proposed as a theoretical result. The remarkable performance of the proposed shrinkage estimator, compared with the sample mean and the James–Stein estimator, is illustrated by a thorough numerical simulation. A real data analysis also witnesses the applicability of the proposed estimator for multivariate time series.

Original languageEnglish
Pages (from-to)733-751
Number of pages19
JournalStatistical Inference for Stochastic Processes
Issue number3
Publication statusPublished - 2021 Oct


  • James–Stein estimator
  • Multivariate stationary processes
  • Sample mean
  • Shrinkage estimation
  • Shrinkage function
  • Spectral density matrix

ASJC Scopus subject areas

  • Statistics and Probability


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