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A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic

  • Morten Ørregaard Nielsen

    ()

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung’s (2002) test as the special case d = 1. It is shown that (i) each member of the family with d > 0 is consistent, (ii) the asymptotic distribution depends on d, and thus reflects the parameter chosen to implement the test, and (iii) since the asymptotic distribution depends on d and the test remains consistent for all d > 0, it is possible to analyze the power of the test for different values of d. The usual Phillips-Perron or Dickey-Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties. It is shown that members of the family with d

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-36.

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Length: 29
Date of creation: 30 Jun 2008
Date of revision:
Handle: RePEc:aah:create:2008-36
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  2. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  3. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  4. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
  5. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(05), pages 765-814, October.
  6. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  7. Breitung, Jorg & Taylor, A. M. Robert, 2003. "Corrigendum to "Nonparametric tests for unit roots and cointegration" [J. Econom. 108 (2002) 343-363]," Journal of Econometrics, Elsevier, vol. 117(2), pages 401-404, December.
  8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  9. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
  10. Vogelsang, Timothy J, 1998. "Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 73-80, January.
  11. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
  12. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
  13. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
  14. Nielsen, Morten, 2008. "A Powerful Tuning Parameter Free Test of the Autoregressive Unit Root Hypothesis," Working Papers 08-05, Cornell University, Center for Analytic Economics.
  15. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  16. Stephen J. Leybourne & Paul Newbold, 1999. "The behaviour of Dickey-Fuller and Phillips-Perron tests under the alternative hypothesis," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 92-106.
  17. 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.
  18. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  19. Shin, Yongcheol & Schmidt, Peter, 1992. "The KPSS stationarity test as a unit root test," Economics Letters, Elsevier, vol. 38(4), pages 387-392, April.
  20. Franses, Philip Hans & Haldrup, Niels, 1994. "The Effects of Additive Outliers on Tests for Unit Roots and Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 471-78, October.
  21. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  22. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  23. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
  24. Agiakloglou, Christos & Newbold, Paul, 1996. "The balance between size and power in Dickey-Fuller tests with data-dependent rules for the choice of truncation lag," Economics Letters, Elsevier, vol. 52(3), pages 229-234, September.
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