Autocovariance Function Estimation via Penalized Regression

• Activity Number: 279
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Lina Liao*+ and Cheolwoo Park and Jan Hannig and Kee-Hoon Kang
• Companies: University of Georgia and University of Georgia and University of North Carolina at Chapel Hill and Hankuk University of Foreign Studies
• Keywords: Autocovariance function ; Asymptotics ; Penalized regression ; Time series

Abstract

The work revisits the autocovariance function estimation, a fundamental problem in statistical inference for time series. We convert the function estimation problem into constrained penalized regression with a generalized penalty that provides us with flexible and accurate estimation, and study the asymptotic properties of the proposed estimator. In case of a nonzero time series, we apply a penalized regression technique to a differenced time series, which does not require a separate detrending procedure. In penalized regression, selection of tuning parameters is critical and we propose four different data-driven criteria for determining them. A simulation study shows effectiveness of the tuning parameter selection and that the proposed approach is superior to some existing methods.