  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.
