Nonlinear Cointegrating Regression under Weak Identification
AbstractAn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1768.
Length: 46 pages
Date of creation: Sep 2010
Date of revision:
Publication status: Published in Econometric Theory (June 2012), 28(3): 509-547
Note: CFP 1355.
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- Shi, Xiaoxia & Phillips, Peter C.B., 2012. "Nonlinear Cointegrating Regression Under Weak Identification," Econometric Theory, Cambridge University Press, vol. 28(03), pages 509-547, June.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-25 (All new papers)
- NEP-ECM-2010-09-25 (Econometrics)
- NEP-ETS-2010-09-25 (Econometric Time Series)
- NEP-ORE-2010-09-25 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
- Giacomini, Raffaella & Granger, Clive W.J., 2001.
"Aggregationn of Space-Time Processes,"
University of California at San Diego, Economics Working Paper Series
qt77f76455, Department of Economics, UC San Diego.
- Donald W.K. Andrews & Xu Cheng, 2011.
"GMM Estimation and Uniform Subvector Inference with Possible Identification Failure,"
Cowles Foundation Discussion Papers
1828, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.
- Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University.
- repec:wyi:journl:002195 is not listed on IDEAS
- Yae In Baek & Jin Seo Cho & Peter C.B. Phillips, 2013. "Testing Linearity Using Power Transforms of Regressors," Cowles Foundation Discussion Papers 1917, Cowles Foundation for Research in Economics, Yale University.
- Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Haiqiang Chen & Ying Fang & Yingxing Li, 2013. "Estimation and Inference for Varying-coefficient Models with Nonstationary Regressors using Penalized Splines," SFB 649 Discussion Papers SFB649DP2013-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If references are entirely missing, you can add them using this form.