On the Marcenko-Pastur law for linear time series

High-dimensional time series arise naturally in econometrics and finance, atmospheric and environmental science, genomics, experimental chemistry, and electrical engineering, among a multitude of disciplines. Recent developments in the statistical analysis of high-dimensional data have demonstrated the limitations of many existing statistical procedures. Exploration of the behavior of some widely used descriptive statistics has resulted in the discovery of new phenomena, and these theoretical developments in turn have contributed to the expanding body of sophisticated statistical procedures geared towards analyzing high-dimensional data. This pursuit benefitted from the confluence of knowledge from various disciplines such as probability theory, optimization, geometry and computer science. Random matrix theory has contributed significantly to the aforementioned theoretical developments. However, until recently, the analysis of serially dependent data did not figure prominently in this discipline. The primary goal of this proposal to introduce the random matrix perspective in the study of multivariate time series, and utilize the resulting theoretical developments to build statistical methodologies for analyzing high-dimensional time series data.