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A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic

  • Nielsen, Morten Ørregaard

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d , and containing the Breitung (2002, Journal of Econometrics 108, 342–363) test as the special case d = 1. It is shown that (a) each member of the family with d > 0 is consistent, (b) the asymptotic distribution depends on d and thus reflects the parameter chosen to implement the test, and (c) because 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 and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 06 (December)
Pages: 1515-1544

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Handle: RePEc:cup:etheor:v:25:y:2009:i:06:p:1515-1544_99
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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
  10. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  11. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  12. 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.
  13. 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.
  14. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  15. Shin, Yongcheol & Schmidt, Peter, 1992. "The KPSS stationarity test as a unit root test," Economics Letters, Elsevier, vol. 38(4), pages 387-392, April.
  16. 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.
  17. Javier Hualde, 2005. "Unbalanced Cointegration," Faculty Working Papers 06/05, School of Economics and Business Administration, University of Navarra.
  18. 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.
  19. 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.
  20. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  21. 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.
  22. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  23. 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.
  24. 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.
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