Specification Testing for Nonlinear Cointegrating Regression
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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.
Wang, Qiying and Phillips, Peter C.B., "Specification Testing for Nonlinear Cointegrating Regression" (2011). Cowles Foundation Discussion Papers. 2120.