Spectral measure of empirical autocovariance matrices of high dimensional Gaussian stationary processes
高维高斯平稳过程经验自协方差矩阵的谱测度
Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain statistical problems, such as those related to testing for white noise. We study the behavior of their spectral measures in the asymptotic regime where the time series dimension and the observation window length both grow to infinity, and at…