  We provide new asymptotic theory for kernel density estimators, when these
are applied to autoregressive processes exhibiting moderate deviations from a
unit root. This fills a gap in the existing literature, which has to date
considered only nearly integrated and stationary autoregressive processes.
These results have applications to nonparametric predictive regression models.
In particular, we show that the null rejection probability of a nonparametric t
test is controlled uniformly in the degree of persistence of the regressor.
This provides a rigorous justification for the validity of the usual
nonparametric inferential procedures, even in cases where regressors may be
highly persistent.
