Model checks for nonlinear cointegrating regression

Using the marked empirical processes, this paper develops a test of parametric specification in a nonlinear cointegrating regression model. Unlike the kernel-smoothed U-statistic considered in Gao et al. (2009) and Wang and Phillips (2012), our new test statistic avoids the use of bandwidth, which has some advantages for practitioners. Simulations and a real data example show that our new test has a good finite sample performance. Other contributions of this paper are to provide a rigorous proof on weak convergence for a class of martingales and construct a simulated estimator of the limiting null distribution, which are interesting in their own rights.