COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1779 Specification Testing for Nonlinear Cointegrating Regression Qiying Wang and Peter C. B. Phillips January 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. |
