NONPARAMETRIC ESTIMATION IN A NONLINEAR COINTEGRATION TYPE MODEL

摘要

We derive an asymptotic theory of nonparametric estimation for a time series regression model Z, = f(X/) + Wt, where [Xt) and (Z() are observed nonstationary processes and {W/} 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 non-stationary 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 /(x) under the assumption that {W/} is a Markov chain satisfying some mixing conditions. The finite-sample properties of f(x) are studied by means of simulation experiments.