On the Marčenko-Pastur law for linear time series

By Haoyang Liu, Alexander Aue, Debashis Paul. 2013

71 citations recorded by the source corpus.

This paper is concerned with extensions of the classical Mar\v{c}enko-Pastur law to time series. Specifically, $p$-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed (real- or complex-valued) entries possessing zero mean, unit variance and finite fourth moments. The coefficient matrices of the linear process are assumed to be simultaneously diagonalizable. In this setting, the limiting behavior of the empirical spectral distribution of both sample covariance and symmetrized sample autocovariance matrices is determined in the high-dimensional setting $p/n\to c\in (0,\infty)$ for which dimension $p$ and sample size $n$ diverge to infinity at the same rate. The results extend existing contributions available in the literature for the covariance case and are one of the first of their kind for the autocovariance case.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b6a0c49a6ee3a385d3b3b718a470611e6540db89

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Citations in the corpus

On testing for high-dimensional white noise (2018, methodology): “Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer, Berlin. Paul, D. and Aue, A. (2014). Random matrix theory in statistics: A review. Journal of Statistical Planning and Inference, 150, 1-29. Sarkar, S. K. and Chang, C. K. (1997). The Simes method for multiple hypothe”