A note on a Marčenko-Pastur type theorem for time series

Abstract

In this note we develop an extension of the Marčenko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for its Stieltjes transform depending on the spectral density of the time series. A numerical algorithm is then given to compute the density functions of these LSD's.

Cited by in corpus (9)

• On the Marčenko-Pastur law for linear time series
• Efficient Computation of Limit Spectra of Sample Covariance Matrices
• Large sample behaviour of high dimensional autocovariance matrices
• Limiting spectral distribution of sample autocovariance matrices
• The universality principle for spectral distributions of sample covariance matrices
• The limiting spectral distribution in terms of spectral density
• CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data
• Singular value distribution of dense random matrices with block Markovian dependence
• Spiked sample covariance matrices with possibly multiple bulk components