Journal
ANNALS OF STATISTICS
Volume 35, Issue 1, Pages 252-299Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053606000001181
Keywords
cointegration; nonstationary time series models; null recurrent Markov chain; nonparametric kernel estimators; transfer function model
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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.
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