Nonlinear Cointegrating Regression under Weak Identification

Xiaoxia Shi and Peter Phillips

No 1768, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.

Keywords: Integrated process; Local time; Nonlinear regression; Uniform weak convergence; Weak identification (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2010-09
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Note: CFP 1355.
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Econometric Theory (June 2012), 28(3): 509-547

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d17/d1768.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Journal Article: NONLINEAR COINTEGRATING REGRESSION UNDER WEAK IDENTIFICATION (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1768

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().