Nonparametric estimation in a nonlinear cointegration type model

We derive an asymptotic theory of nonparametric estimation for an nonlinear transfer function model Z(t) = f (Xt) + Wt where {Xt} and {Zt} are observed nonstationary processes and {Wt} is a stationary process. IN econometrics this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results have wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent.. Markov chains. This subclass contains the random walk model and the unit root processes. WE derive the asymptotics of an nonparametric estimate of f(z) under two alternative sets of assumptions on {Wt}: i) {Wt} is a linear process ii) {Wt} is a Markov chain satisfying some mixing conditions. The latter requires considerably more work but also holds larger promise for further developments. The finite sample properties f(x) are studied via a set of simulation experiments.