A Thresholding-Based Prewhitened Long-Run Variance Estimator and Its Dependence-Oracle Property

• Activity Number: 402 - Variance, Change Points, and Outliers
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ting Zhang*
• Companies: Boston University
• Keywords: long-run variance ; thresholding ; prewhitening

Abstract

Statistical inference of time series data routinely relies on the estimation of long-run variances, defined as the sum of autocovariances of all orders. We consider a new class of long-run variance estimators, which first soaks up the dependence by a decision-based prewhitening filter, then regularizes autocorrelations of the resulting residual process by thresholding, and finally recolors back to obtain an estimator of the original process. Under mild regularity conditions, we prove that the proposed estimator (i) consistently estimates the long-run variance; (ii) achieves the parametric convergence rate when the underlying process has a sparse dependence structure as in finite-order moving average models; and (iii) enjoys the dependence-oracle property in the sense that it will automatically reduce to the sample variance if the data are actually independent. Monte Carlo simulations are conducted to examine its finite-sample performance and make comparisons with existing estimators.