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

By Jianfeng Yao. 2011

62 citations recorded by the source corpus.

In this note we develop an extension of the Marcenko–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.

Subfields: Condensed Matter Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0654b02d2835a80aa205ed5e775004bc7698b38e

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In Condensed Matter Physics

In Statistics and Probability

Citations in the corpus

Random matrix theory in statistics: A review (2014, background): “Further applications include proving the existence of the limiting ESD of a sample covariance matrix when the columns of Yn are i.i.d. stationary time series, e.g., a causal VARMA process (Jin et al., 2009), and more generally, a linear process (Pfaffel and Schlemm, 2012; Yao, 2012).”
On the Marčenko-Pastur law for linear time series (2013, background): “1 reduces to the results obtained in Pfaffel and Schlemm [32] and Yao [35].”
On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries (2015, background): “Bai and Zhou [3], Yao [18], Banna and Merlevède [4] and Merlevède and Peligrad [14], among others, treated large covariance matrices based on an independent structure between columns and correlated random variables in rows.”