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.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 28 (2012)
Issue (Month): 03 (June)
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Other versions of this item:
- Xiaoxia Shi & Peter C. B. Phillips, 2010. "Nonlinear Cointegrating Regression under Weak Identification," Cowles Foundation Discussion Papers 1768, Cowles Foundation for Research in Economics, Yale University.
- 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
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.:
- Raffaella Giacomini & Clive W.J. Granger, 2002.
"Aggregation of Space-Time Processes,"
Boston College Working Papers in Economics
582, Boston College Department of Economics.
- 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.
- Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
- 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.
- 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.
- 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.
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