Regularization and Prediction of Long-Memory Time Series

• Activity Number: 53
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: General Methodology
• Author(s): Wilfredo Palma*+ and Mohsen Pourahmadi
• Companies: Pontificia Universidad Católica de Chile and Texas A&M University
• Keywords: Banding ; Consistency ; Long-range dependence

Abstract

In this talk we consider the estimation of covariance matrices of long-memory stationary processes via banding, i.e. replacing by zero the smaller and less reliable sample autocovariances corresponding to larger lags. For short-memory processes it is known that the sample covariance matrix is not a consistent estimator of its population counterpart in the operator norm. While banded estimators are consistent for short-memory processes under mild conditions (Wu and Pourahmadi, 2009), the problem is open at this time for long-memory processes, but seems to be more hopeful for the banded inverse covariance matrix. We emphasize the important role of increasing order AR model fitting in the banded estimation of the inverse covariance matrix and recast the Haslett and Raftery (1989) approximation of finite predictors of long-memory processes as banding/tapering the Cholesky factor of the inverse covariance matrix. The results are applied to the classical linear prediction problems and their performance is assessed by means of simulations and real time series data.