Robust estimation in a nonlinear cointegration model

This paper considers the nonparametric M -estimator in a nonlinear cointegration type model. The local time density argument, which was developed by Phillips and Park (1998) [6] and Wang and Phillips (2009) [9], is applied to establish the asymptotic theory for the nonparametric M -estimator. The weak consistency and the asymptotic distribution of the proposed estimator are established under mild conditions. Meanwhile, the asymptotic distribution of the local least squares estimator and the local least absolute distance estimator can be obtained as applications of our main results. Furthermore, an iterated procedure for obtaining the nonparametric M -estimator and a cross-validation bandwidth selection method are discussed, and some numerical examples are provided to show that the proposed methods perform well in the finite sample case.