Consistency of Large Autocovariance Matrices

Event Date: 

Tuesday, October 21, 2014 - 3:30pm to 5:00pm

Event Date Details: 

Refreshments served at 3:15 PM

Event Location: 

  • South Hall 5607F

Dr. Sreenivas Konda (UCSB)

Title: Consistency of Large Autocovariance Matrices

Abstract:We consider Autoregressive (AR) processes of large p, but less than n, to approximate a linear time series. Using Bartlett's formula and strong mixing conditions, we show the consistency of the large sample autocovariance matrix by banding procedure. These large sample autocovariance matrices are consistent in operator norm as long as (log p)/n goes to 0. Parameters of large AR(p) model are estimated using a regularization procedure and banding of the autocovariance matrix. We also briefly review application of banding in finding the inverse of sum of two special matrices. Real examples from physics and business  are used to illustrate the proposed methods.