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Dynamic misspecification in nonparametric cointegrating regression

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  • Kasparis, Ioannis
  • Phillips, Peter C.B.

Abstract

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya–Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a “pseudo-true function” limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-true function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification (hn, h is a bandwidth term) but the variance of the limit distribution is larger. The practical import of the results for index models, functional regression models, temporal aggregation and specification testing are discussed. Two nonparametric linearity tests are considered. The proposed tests are robust to dynamic misspecification. Under the null hypothesis (linearity), the first test has a χ2 limit distribution while the second test has limit distribution determined by the maximum of independently distributed χ2 variates. Under the alternative hypothesis, the test statistics attain a hn divergence rate.

Suggested Citation

  • Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
  • Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:270-284 DOI: 10.1016/j.jeconom.2012.01.037
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    2. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    3. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, pages 104-117.
    4. Qiying Wang & Peter C.B. Phillips & Ioannis Kasparis, 2017. "Latent Variable Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 3011, Cowles Foundation for Research in Economics, Yale University.
    5. Yichen Gao & Zheng Li & Zhongjian Lin, 2014. "Semiparametric Estimation of Partially Linear Varying Coefficient Models with Time Trend and Nonstationary Regressors," Emory Economics 1412, Department of Economics, Emory University (Atlanta).
    6. Banerjee Anurag & Pitarakis Jean-Yves, 2014. "Functional cointegration: definition and nonparametric estimation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 1-14, December.
    7. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, pages 270-284.
    8. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
    9. 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.

    More about this item

    Keywords

    Dynamic misspecification; Functional regression; Integrable function; Integrated process; Linearity test; Local time; Misspecification; Mixed normality; Nonlinear cointegration; Nonparametric regression;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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