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Specification Testing for Nonlinear Cointegrating Regression

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Abstract

We provide a limit theory for a general class of kernel smoothed U statistics that may be used for specification testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and useful in other applications.

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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1779.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1779.

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Length: 66 pages
Date of creation: Jan 2011
Date of revision: Feb 2011
Publication status: Published in The Annals of Statistics (2012), 40(2): 2, 727–758
Handle: RePEc:cwl:cwldpp:1779

Note: CFP 1359
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Related research

Keywords: Intersection local time; Kernel regression; Nonlinear nonparametric model; Ornstein-Uhlenbeck process; Specification tests; Weak convergence;

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  1. de Jong, Robert & Wang, Chien-Ho, 2005. "Further Results On The Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 21(02), pages 413-430, April.
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Cited by:
  1. Liew, Venus Khim-Sen & Ling, Tai-Hu & Chia, Ricky Chee-Jiun & Yoon, Gawon, 2012. "On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea," Economic Modelling, Elsevier, vol. 29(2), pages 326-332.

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