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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.

Suggested Citation

  • Qiying Wang & Peter C.B. Phillips, 2011. "Specification Testing for Nonlinear Cointegrating Regression," Cowles Foundation Discussion Papers 1779, Cowles Foundation for Research in Economics, Yale University, revised Feb 2011.
    • Handle: RePEc:cwl:cwldpp:1779
    Note: CFP 1359
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d17/d1779.pdf
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    References listed on IDEAS

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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(2), 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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    More about this item

    Keywords

    Intersection local time; Kernel regression; Nonlinear nonparametric model; Ornstein-Uhlenbeck process; Specification tests; Weak convergence;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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