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 f̂(x) are studied by means of simulation experiments.
Publié le : 2007-02-14
Classification:
Cointegration,
nonstationary time series models,
null recurrent Markov chain,
nonparametric kernel estimators,
transfer function model,
62M10,
62G08,
91B84,
60J05
@article{1181100188,
author = {Karlsen, Hans Arnfinn and Myklebust, Terje and Tj\o stheim, Dag},
title = {Nonparametric estimation in a nonlinear cointegration type model},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 252-299},
language = {en},
url = {http://dml.mathdoc.fr/item/1181100188}
}
Karlsen, Hans Arnfinn; Myklebust, Terje; Tjøstheim, Dag. Nonparametric estimation in a nonlinear cointegration type model. Ann. Statist., Tome 35 (2007) no. 1, pp. 252-299. http://gdmltest.u-ga.fr/item/1181100188/