In this paper, we study a nonlinear cointegration type model Yκ = m(Xκ) + wκ, where {Yκ} and {Xκ} are observed nonstationary processes and {Wκ} is an unobserved stationary process. The process {Xκ} is assumed to be a null-recurrent Markov chain. We apply a robust version of local linear regression smoothers to estimate m(-). Under mild conditions, the uniform weak consistency and asymptotic normality of the local linear M-estimators are established. Furthermore, a one-step iterated procedure is introduced to obtain the local linear M-estimator and the optimal bandwidth selection is discussed. Meanwhile, some numerical examples are given to show that the proposed theory and methods perform well in practice
