Nonparametric estimation in a nonlinear cointegration type model

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. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results are of wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent Markov chains. This subclass contains random walk, unit root processes and nonlinear processes. We derive the asymptotics of a nonparametric estimate of f (x) under the assumption that {W-t} is a Markov chain satisfying some mixing conditions. The finite-sample properties of (f) over cap (x) are studied by means of simulation experiments.