Nonparametric regression estimation in a null recurrent time series

Abstract

We derive an asymptotic theory of nonparametric estimation for a time series regression model Z t = f( X t )+ W t , where { X t } and { Z t } are observed nonstationary processes, and { W t } is an unobserved stationary process. The class of nonstationary processes allowed for { X t } is a subclass of the class of null recurrent Markov chains. This subclass contains the random walk, unit root processes and nonlinear processes. The process { W t } is assumed to be linear and stationary.