Transition Matrix Estimation in High Dimensional Time Series_pdf.pdf

Transition Matrix Estimation in High Dimensional Time Series Fang Han ******@ Johns Hopkins University, 615 Street, Baltimore, MD 21205 USA Han Liu ******@ Princeton University, 98 Charlton Street, Princeton, NJ 08544 USA Abstract In this paper, we propose a new method in estimating transition matrices of high dimen- sional vector autoregressive (VAR) models. Here the data are assumed e from a stationary Gaussian VARtime series. By for- mulating the problem as a linear program, we provide a new approach to conduct in- ference on such models. In theory, under a doubly asymptotic framework in which both the sample sizeTand dimensionalitydof the time series can increase (with possibly d?T), we provide explicit rates of conver- gence between the estimator and the popu- lation transition matrix under di?erent ma- trix norms. Our results show that the spec- tral norm of the transition matrix plays a pivotal role in determining the ?nal rates of convergence. This is the ?rst work analyz- ing the estimation of transition matrices un- der a high dimensional doubly asymptotic framework. Experiments are conducted on both synthetic and real-world stock data to demonstrate the e?ectiveness of the proposed pared with the existing methods. The results of this paper have broad impact on di?erent applications, including ?nance, genomics, and brain imaging. 1. Introdu