Publication Date: January 2011
Revision Date: June 2011
We provide a limit theory for a general class of kernel smoothed U statistics that may be used for speciﬁcation testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or near unit roots. The limit theory for the speciﬁcation test depends on the self intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and useful in other applications.
Intersection local time, Kernel regression, Nonlinear nonparametric model, Ornstein-Uhlenbeck process, Speciﬁcation tests, Weak convergence
JEL Classification Codes: C14, C22