IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Dynamic misspecification in nonparametric cointegrating regression

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

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0304407612000474
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 168 (2012)
Issue (Month): 2 ()
Pages: 270-284

as
in new window

Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:270-284
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

References listed on IDEAS
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.:

as in new window
  1. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," NBER Working Papers 10914, National Bureau of Economic Research, Inc.
  2. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
  3. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
  4. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  5. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
  6. Yoosoon Chang & Joon Y. Park & Peter C.B. Phillips, 1999. "Nonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors," Cowles Foundation Discussion Papers 1245, Cowles Foundation for Research in Economics, Yale University.
  7. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
  8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  9. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," CIRANO Working Papers 2004s-20, CIRANO.
  10. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
  11. Russell Davidson & James G. MacKinnon, 1980. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Working Papers 378, Queen's University, Department of Economics.
  12. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  13. Sydney Ludvigson & Serena Ng, 2006. "The Empirical Risk-Return Relation: a factor analysis approach," 2006 Meeting Papers 236, Society for Economic Dynamics.
  14. Emmanuel Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series," Working Papers 2004-22, Centre de Recherche en Economie et Statistique.
  15. Berkes, Istv n & Horv th, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(02), pages 304-322, April.
  16. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
  17. Peter C.B. Phillips, 2008. "Local Limit Theory and Spurious Nonparametric Regression," Cowles Foundation Discussion Papers 1654, Cowles Foundation for Research in Economics, Yale University.
  18. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
  19. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  20. Peter C.B. Phillips & Joon Y. Park, 1999. "Nonstationary Binary Choice," Cowles Foundation Discussion Papers 1223, Cowles Foundation for Research in Economics, Yale University.
  21. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
  22. Peter C.B. Phillips, 1999. "Descriptive Econometrics for Nonstationary Time Series with Empirical Illustrations," Cowles Foundation Discussion Papers 1219, Cowles Foundation for Research in Economics, Yale University.
  23. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
  24. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  25. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," University of California at Los Angeles, Anderson Graduate School of Management qt9mf223rs, Anderson Graduate School of Management, UCLA.
  26. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
  27. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
  28. Kasparis, Ioannis, 2011. "Functional Form Misspecification In Regressions With A Unit Root," Econometric Theory, Cambridge University Press, vol. 27(02), pages 285-311, April.
  29. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
  30. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:168:y:2012:i:2:p:270-284. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.