Publication Type

Journal Article

Publication Date

6-2012

Abstract

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-true function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification (hn, h is a bandwidth term) but the variance of the limit distribution is larger. The practical import of the results for index models, functional regression models, temporal aggregation and specification testing are discussed. Two nonparametric linearity tests are considered. The proposed tests are robust to dynamic misspecification. Under the null hypothesis (linearity), the first test has a χ2 limit distribution while the second test has limit distribution determined by the maximum of independently distributed χ2 variates. Under the alternative hypothesis, the test statistics attain a hn divergence rate.

Keywords

Dynamic misspecification, Functional regression, Integrable function, Integrated process, Linearity test, Local time, Misspecification, Mixed normality, Nonlinear cointegration, Nonparametric regression

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

168

Issue

2

First Page

270

Last Page

284

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2012.01.037

Publisher

Elsevier

Embargo Period

8-5-2017

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://doi.org/10.1016/j.jeconom.2012.01.037

Included in

Econometrics Commons

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