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

摘要: Abstract Let S = (1/ n ) Σ t=1 X ( t )′, where (1), …, are p × 1 random vectors with mean zero. When 1, independently and identically distributed (i.i.d.) as multivariate normal vector 0 covariance matrix Σ, many authors have investigated the asymptotic expansions for distributions of various functions eigenvalues . In this paper, we will extend above results to case when { )} is a Gaussian stationary process. Also shall derive certain sample canonical correlations in time series. Applications some signal processing also discussed.