The Annals of Statistics

Nonparametric estimation in a nonlinear cointegration type model

Hans Arnfinn Karlsen, Terje Myklebust, and Dag Tjøstheim

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

Article information

Ann. Statist., Volume 35, Number 1 (2007), 252-299.

First available in Project Euclid: 6 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G08: Nonparametric regression 91B84: Economic time series analysis [See also 62M10]
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Cointegration nonstationary time series models null recurrent Markov chain nonparametric kernel estimators transfer function model


Karlsen, Hans Arnfinn; Myklebust, Terje; Tjøstheim, Dag. Nonparametric estimation in a nonlinear cointegration type model. Ann. Statist. 35 (2007), no. 1, 252--299. doi:10.1214/009053606000001181.

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