Nonparametric estimation in a nonlinear cointegration type model

TL;DR

This paper develops an asymptotic theory for nonparametric estimation in nonlinear cointegration models with nonstationary regressors, extending to processes like random walks and unit roots, with simulation validation.

Contribution

It introduces a new asymptotic framework for nonparametric estimation in nonlinear cointegration models involving null recurrent Markov chains.

Findings

Asymptotic properties of the estimator are derived.

Simulation studies demonstrate finite-sample performance.

Results apply to a broad class of nonstationary processes.

Abstract

We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{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 $\{X_t\}$ 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 $\hat{f}(x)$ are studied by means of simulation experiments.