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Asymptotic distributions of functions of the eigenvalues of sample covariance matrix and canonical correlation matrix in multivariate time series

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  • Taniguchi, M.
  • Krishnaiah, P. R.

Abstract

Let S = (1/n) [Sigma]t=1n X(t) X(t)', where X(1), ..., X(n) are p - 1 random vectors with mean zero. When X(t) (t = 1, ..., n) are independently and identically distributed (i.i.d.) as multivariate normal with mean vector 0 and covariance matrix [Sigma], many authors have investigated the asymptotic expansions for the distributions of various functions of the eigenvalues of S. In this paper, we will extend the above results to the case when {X(t)} is a Gaussian stationary process. Also we shall derive the asymptotic expansions for certain functions of the sample canonical correlations in multivariate time series. Applications of some of the results in signal processing are also discussed.

Suggested Citation

  • Taniguchi, M. & Krishnaiah, P. R., 1987. "Asymptotic distributions of functions of the eigenvalues of sample covariance matrix and canonical correlation matrix in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 156-176, June.
    • Handle: RePEc:eee:jmvana:v:22:y:1987:i:1:p:156-176
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    Cited by:

    1. Xinyu Zhang & Howell Tong, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 543-565, April.
    2. Yan Liu & Masanobu Taniguchi, 2021. "Minimax estimation for time series models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 353-359, December.
    3. Zhang, Xinyu & Tong, Howell, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," LSE Research Online Documents on Economics 113566, London School of Economics and Political Science, LSE Library.

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