ON THE MARCENKO-PASTUR LAW FOR LINEAR TIME SERIES

• 成果类型: Article
• 署名作者: Liu, Haoyang; Aue, Alexander; Paul, Debashis
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1294
• 发表日期: 2015
• 页码: 675-712
• 关键词: dynamic-factor model; sample covariance matrices; Spectral Distribution; eigenvalues; number

摘要

This paper is concerned with extensions of the classical Marcenko-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 --> c is an element of(0, infinity) 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.