Reduced-Rank Covariance Estimation in Vector Autoregressive Modeling

• Activity Number: 334
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Richard A. Davis* and Pengfei Zang and Tian Zheng
• Companies: Columbia University and Columbia University and Columbia University
• Keywords: VAR models ; Covariance estimation ; matrix decomposition

Abstract

We consider reduced-rank modeling of the white noise covariance matrix in a large dimensional vector autoregressive (VAR) model. We first propose the reduced-rank covariance estimator under the setting where independent observations are available. We derive the reduced-rank estimator based on a latent variable model for the observation vector and give the analytical form of its maximum likelihood estimate. Simulation results show that the reduced-rank covariance estimator outperforms two competing covariance estimators for estimating large dimensional covariance matrices from independent observations. Then we describe how to integrate the proposed reduced-rank estimator into the fitting of large dimensional VAR models, where we consider two scenarios that require different model fitting procedures. In the VAR modeling context, our reduced-rank covariance estimator not only provides interpretable descriptions of the dependence structure of VAR processes but also leads to improvement in model-fitting and forecasting over unrestricted covariance estimators. Two real data examples are presented to illustrate these fitting procedures.