Finite Sample Properties of Tests Based on Prewhitened Nonparametric Covariance Estimators

TL;DR

This paper analytically examines the size and power of autocorrelation-corrected F-tests using prewhitened nonparametric covariance estimators in linear regression with dependent errors, revealing limitations and proposing an adjustment method.

Contribution

It provides a theoretical analysis of the size and power properties of these tests and introduces a simple adjustment to improve their performance.

Findings

Tests often suffer from size distortions or low power.

A simple adjustment with artificial regressors can mitigate these issues.

The analysis applies to a broad class of design matrices.

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.