Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model

The explicit representation for the limiting spectral moments of sample covariance matrices generated by the periodic autoregressive model (PAR) is established. We propose to use the moment-constrained maximum entropy method to estimate the spectral density function. The experiments show that the maximum entropy spectral density function curve obtained based on the fourth-order limiting spectral moment can match histograms of the eigenvalues of the covariance matrices very well.