Nonparametric estimation in a nonlinear cointegration type model

Details Nonparametric estimation in a nonlinear cointegration type model Nonparametric estimation in a nonlinear cointegration type model

2007-08-03

arxiv.org/abs/0708.0503v1

Annals of Statistics 2007, Vol. 35, No. 1, 252-299

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001181 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001181

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.

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