Publication Type
Journal Article
Version
acceptedVersion
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
Citation
KASPARIS, Ioannis and PHILLIPS, Peter C. B..
Dynamic misspecification in nonparametric cointegrating regression. (2012). Journal of Econometrics. 168, (2), 270-284.
Available at: https://ink.library.smu.edu.sg/soe_research/1975
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.jeconom.2012.01.037