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A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors

  • Jiti Gao

    ()

  • Maxwell King

    ()

This paper considers a class of parametric models with nonparametric autoregressive errors. A new test is proposed and studied to deal with the parametric specification of the nonparametric autoregressive errors with either stationarity or nonstationarity. Such a test procedure can initially avoid misspecification through the need to parametrically specify the form of the errors. In other words, we propose estimating the form of the errors and testing for stationarity or nonstationarity simultaneously. We establish asymptotic distributions of the proposed test. Both the setting and the results differ from earlier work on testing for unit roots in parametric time series regression. We provide both simulated and real-data examples to show that the proposed nonparametric unit-root test works in practice.

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File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp20-11.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 20/11.

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Length: 40 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-20
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  1. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 475-495.
  2. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
  3. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
  4. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  5. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  6. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.
  7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  8. Chen, Song Xi & Gao, Jiti, 2007. "An adaptive empirical likelihood test for parametric time series regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 950-972, December.
  9. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  10. Dirk Te Velde, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers 178, National Institute of Economic and Social Research.
  11. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  12. Jiti Gao & Irene Gijbels, 2009. "Bandwidth Selection in Nonparametric Kernel Testing," School of Economics Working Papers 2009-01, University of Adelaide, School of Economics.
  13. Markus Frölich, 2008. "Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables," International Statistical Review, International Statistical Institute, vol. 76(2), pages 214-227, 08.
  14. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
  15. Jiti Gao & Maxwell King & Zudi Lu & Dag Tjøstheim, 2009. "Nonparametric Specification Testing for Nonlinear Time Series with Nonstationarity," School of Economics Working Papers 2009-03, University of Adelaide, School of Economics.
  16. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
  17. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  18. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  19. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(05), pages 844-882, October.
  20. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  21. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR-GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, 05.
  22. Granger, Clive W. J. & Inoue, Tomoo & Morin, Norman, 1997. "Nonlinear stochastic trends," Journal of Econometrics, Elsevier, vol. 81(1), pages 65-92, November.
  23. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  24. Li, Q. & Hsiao, C., 1998. "Testing serial correlation in semiparametric panel data models," Journal of Econometrics, Elsevier, vol. 87(2), pages 207-237, September.
  25. Jia Chen & Jiti Gao & Degui Li, 2009. "Semiparametric Regression Estimation in Null Recurrent Nonlinear Time Series," School of Economics Working Papers 2009-02, University of Adelaide, School of Economics.
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