  Testing restrictions on regression coefficients in linear models often
requires correcting the conventional F-test for potential heteroskedasticity or
autocorrelation amongst the disturbances, leading to so-called
heteroskedasticity and autocorrelation robust test procedures. These procedures
have been developed with the purpose of attenuating size distortions and power
deficiencies present for the uncorrected F-test. We develop a general theory to
establish positive as well as negative finite-sample results concerning the
size and power properties of a large class of heteroskedasticity and
autocorrelation robust tests. Using these results we show that
nonparametrically as well as parametrically corrected F-type tests in time
series regression models with stationary disturbances have either size equal to
one or nuisance-infimal power equal to zero under very weak assumptions on the
covariance model and under generic conditions on the design matrix. In addition
we suggest an adjustment procedure based on artificial regressors. This
adjustment resolves the problem in many cases in that the so-adjusted tests do
not suffer from size distortions. At the same time their power function is
bounded away from zero. As a second application we discuss the case of
heteroskedastic disturbances.
