Local linear M-estimators in null recurrent time series

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.Zhengyan Lin, Degui Li and Jia Chenhttp://www3.stat.sinica.edu.tw/statistica/j19n4/19-4.htm