Abstract:
We study optimal bandwidth selection in nonparametric cointegrating regression
where the regressor is a stochastic trend process driven by short or long memory
innovations. Unlike stationary regression, the optimal bandwidth is found to be a
random sequence which depends on the sojourn time of the process. All random
sequences hn that lie within a wide band of rates as the sample size n → ∞ have
the property that local level and local linear kernel estimates are asymptotically
normal, which enables inference and conveniently corresponds to limit theory in
the stationary regression case. This finding reinforces the distinctive flexibility of
data-based nonparametric regression procedures for nonstationary nonparametric
regression. The present results are obtained under exogenous regressor conditions,
which are restrictive but which enable flexible data-based methods of practical
implementation in nonparametric predictive regressions within that environment.