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Karlsen, Hans Arnfinn; Myklebust, Terje; Tjøstheim, Dag

Nonparametric estimation in a nonlinear cointegration type model. (English) Zbl 1114.62089

Ann. Stat. 35, No. 1, 252-299 (2007).
Summary: 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 \(\{X_t\}\) 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 \(\widehat{f(x)}\) are studied by means of simulation experiments.

Cited in 67 Documents

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62M05 Markov processes: estimation; hidden Markov models
91B84 Economic time series analysis

Keywords:

cointegration; nonstationary time series models; null recurrent Markov chain; nonparametric kernel estimators; transfer function model
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References:

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