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Dynamic Misspecification in Nonparametric Cointegrating Regression

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  • Peter C.B.Phillips

    (Yale University, University of Auckland,University of York & Singapore Management University)

  • Ioannis Kasparis

    (University of Cyprus)

Abstract

Linear cointegration is known to have the important property of invariance un- der temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspeci?ed lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspeci?ed lag structure are de- rived, showing the NW estimator to be inconsistent with a ?pseudo-true function? limit that is a local average of the true regression function. In this respect nonlin- ear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-function and ap- propriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct speci?cation but the variance of the limit distribution is larger. Some applications of the limit the- ory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed.

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Bibliographic Info

Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-01-2009.

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Length: 32 Pages
Date of creation: Jan 2009
Date of revision:
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-01-2009

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Keywords: Dynamic misspeci?cation; Functional regression; Integrable function; Integrated process; Local time; Misspeci?cation; Mixed normality; Nonlinear cointe- gration; Nonparametric regression;

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References

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Citations

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Cited by:
  1. Yichen Gao & Zheng Li & Zhongjian Lin, 2014. "Semiparametric Estimation of Partially Linear Varying Coefficient Models with Time Trend and Nonstationary Regressors," Emory Economics, Department of Economics, Emory University (Atlanta) 1412, Department of Economics, Emory University (Atlanta).
  2. Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 8/14, Monash University, Department of Econometrics and Business Statistics.
  3. Pitarakis, Jean-Yves, 2012. "Functional cointegration: definition and nonparametric estimation," MPRA Paper 38846, University Library of Munich, Germany.
  4. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, Elsevier, vol. 176(1), pages 59-79.
  5. Peter C.B.Phillips & Ioannis Kasparis, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," Working Papers, Sim Kee Boon Institute for Financial Economics CoFie-01-2009, Sim Kee Boon Institute for Financial Economics.
  6. 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, Elsevier, vol. 29(2), pages 326-332.

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