  This paper presents uniform convergence rates for kernel regression
estimators, in the setting of a structural nonlinear cointegrating regression
model. We generalise the existing literature in three ways. First, the domain
to which these rates apply is much wider than has been previously considered,
and can be chosen so as to contain as large a fraction of the sample as desired
in the limit. Second, our results allow the regression disturbance to be
serially correlated, and cross-correlated with the regressor; previous work on
this problem (of obtaining uniform rates) having been confined entirely to the
setting of an exogenous regressor. Third, we permit the bandwidth to be
data-dependent, requiring only that it satisfy certain weak asymptotic
shrinkage conditions. Our assumptions on the regressor process are consistent
with a very broad range of departures from the standard unit root
autoregressive model, allowing the regressor to be fractionally integrated, and
to have an infinite variance (and even infinite lower-order moments).
