Eigenvalues of Covariance Matrices of High-Dimensional Time Series

• Activity Number: 600 - High-Dimensional Time Series and Applications in Social and Biological Sciences
• Type: Invited
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Alexander Aue* and Haoyang Liu and Debashis Paul
• Companies: University of California, Davis and University of California, Berkeley and University of California, Davis
• Keywords: Random matrix theory ; Stieltjes transform ; Mean-variance frontier ; Time series ; High-dimensional statistics

Abstract

In this talk the limiting spectral behavior of the covariance and symmetrized autocovariance matrices of a class of high-dimensional linear time series is discussed, where the asymptotic regime is such that dimensionality and sample size grow proportionally. The results extend the classical Marcenko-Pastur law to the time series case. The form of the limiting spectral distribution is exploited to estimate the mean-variance frontier, an important measure of the minimum risk required for a fixed expected return in a portfolio of financial assets. The results may help alleviate the risk underestimation of the mean-variance frontier well documented in the finance and econometrics literature. The talk is based on joint work with Haoyang Liu (UC Berkeley) and Debashis Paul (UC Davis).