Nonparametric estimation in a nonlinear cointegration type model

• 成果类型: Article
• 署名作者: Karlsen, Hans Arnfinn; Myklebust, Terje; Tjostheim, Dag
• 署名单位: University of Bergen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001181
• 发表日期: 2007
• 页码: 252-299
• 关键词: berry-esseen theorem; error-correction; united-kingdom; Money demand

摘要

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.