Open Access
February 2007 Nonparametric estimation in a nonlinear cointegration type model
Hans Arnfinn Karlsen, Terje Myklebust, Dag Tjøstheim
Ann. Statist. 35(1): 252-299 (February 2007). DOI: 10.1214/009053606000001181


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.


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Hans Arnfinn Karlsen. Terje Myklebust. Dag Tjøstheim. "Nonparametric estimation in a nonlinear cointegration type model." Ann. Statist. 35 (1) 252 - 299, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62089
MathSciNet: MR2332276
Digital Object Identifier: 10.1214/009053606000001181

Primary: 62G08 , 62M10 , 91B84
Secondary: 60J05

Keywords: cointegration , nonparametric kernel estimators , Nonstationary time series models , null recurrent Markov chain , transfer function model

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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