Local linear M-estimators in null recurrent time series

Abstract

In this paper, we study a nonlinear cointegration type model , where and are observed nonstationary processes and is an unobserved stationary process. The process is assumed to be a null-recurrent Markov chain. We apply a robust version of local linear regression smoothers to estimate . 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.