Finite Sample Properties of Tests Based on Prewhitened Nonparametric Covariance Estimators

• Activity Number: 490
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): David Preinerstorfer*
• Companies: University of Vienna
• Keywords: Autocorrelation robustness ; Prewhitening ; HAC test ; Size distortion ; Power deficiency ; Artificial regressors

Abstract

We analytically investigate size and power properties of a popular family of procedures for testing linear restrictions on the coefficient vector in a linear regression model with temporally dependent errors. The tests considered are autocorrelation-corrected F-type tests based on prewhitened nonparametric covariance estimators that possibly incorporate a data-dependent bandwidth parameter, e.g., estimators as considered in Andrews and Monahan (1992), Newey and West (1994), or Rho and Shao (2013). For design matrices that are generic in a measure theoretic sense we prove that these tests either suffer from extreme size distortions or from strong power deficiencies. Despite this negative result we demonstrate that a simple adjustment procedure based on artificial regressors can often resolve this problem.