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A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors

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  • Jiti Gao

    ()

  • Maxwell King

    ()

Abstract

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://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp20-11.pdf
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Bibliographic Info

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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Keywords: Autoregressive process; nonlinear time series; nonparametric method; random walk; semiparametric model; unit root test.;

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References

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  1. 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.
  2. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  3. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  5. 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.
  6. 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.
  7. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  8. 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.
  9. 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.
  10. 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.
  11. Mika Meitz & Pentti Saikkonen, 2007. "Stability of nonlinear AR-GARCH models," Economics Series Working Papers 328, University of Oxford, Department of Economics.
  12. 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.
  13. Jiti Gao & Irene Gijbels, 2009. "Bandwidth Selection in Nonparametric Kernel Testing," School of Economics Working Papers 2009-01, University of Adelaide, School of Economics.
  14. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  15. 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.
  16. 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.
  17. Granger, Clive W. J. & Inoue, Tomoo & Morin, Norman, 1997. "Nonlinear stochastic trends," Journal of Econometrics, Elsevier, vol. 81(1), pages 65-92, November.
  18. 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.
  19. Li, Q. & Hsiao, C., 1998. "Testing serial correlation in semiparametric panel data models," Journal of Econometrics, Elsevier, vol. 87(2), pages 207-237, September.
  20. Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 475-95, July.
  21. Gao, Jiti & King, Maxwell & Lu, Zudi & Tjøstheim, Dag, 2009. "Nonparametric Specification Testing For Nonlinear Time Series With Nonstationarity," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1869-1892, December.
  22. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(05), pages 844-882, October.
  23. n/a, 2001. "Balance of payments prospects in EMU," NIESR Discussion Papers 164, National Institute of Economic and Social Research.
  24. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
  25. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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Cited by:
  1. Peter C.B. Phillips & Degui Li & Jiti Gao, 2013. "Estimating Smooth Structural Change in Cointegration Models," Cowles Foundation Discussion Papers 1910, Cowles Foundation for Research in Economics, Yale University.

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