Consistency of Large Sample Autocovariance Matrices

• Activity Number: 228
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Sreenivas Konda*+
• Companies: University of California, Santa Barbara
• Keywords: Large covariance matrix ; Consistency ; Strong mixing ; Bartlett's formula ; Linear time series

Abstract

Autoregressive (AR) time series of unknown order but large p are considered to ?t the data generated by a linear process. We estimate the parameters using a regularization method and show the consistency of sample autocovariance matrix by the popular banding procedure using strong mixing conditions. We derive that these estimates are consistent in Frobenius and operator norms as long as (p/n) goes to zero and obtain explicit convergence rates by three di?erent methods. These convergence rates are studied numerically on a simulated example.