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Trend and initial condition in stationarity tests: the asymptotic analysis

  • Anton Skrobotov

    (Gaidar Institute for Economic Policy)

In this paperwe investigate the behavior of stationarity tests proposed by Muller (2005) and Harris et al. (2007) with uncertainty over the trend and/or initial condition. As dierent tests are e cient for dierent magnitudes of local trend and initial condition, following Harvey et al. (2012) we propose decision rule based on the rejection of null hypothesis for multiple tests. Additionally, we propose a modi cation of this decision rule, relying on additional information about the magnitudes of the local trend and/or the initial condition that is obtained through pre-testing. The resulting modification has satisfactory size properties under both uncertainty types.

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File URL: http://www.iep.ru/files/RePEc/gai/wpaper/0048Skrobotov.pdf
File Function: Revised version, 2012
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Paper provided by Gaidar Institute for Economic Policy in its series Working Papers with number 0048.

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Length: 20 pages
Date of creation: 2012
Date of revision: 2013
Handle: RePEc:gai:wpaper:0048
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  1. Pierre Perron & Tomoyoshi Yabu, 2007. "Estimating Deterministic Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-020, Boston University - Department of Economics.
  2. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
  3. Harris, David & Leybourne, Stephen & McCabe, Brendan, 2007. "Modified Kpss Tests For Near Integration," Econometric Theory, Cambridge University Press, vol. 23(02), pages 355-363, April.
  4. Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
  5. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2006. "A simple, robust and powerful test of the trend hypothesis," Discussion Papers 06/01, University of Nottingham, Granger Centre for Time Series Econometrics.
  6. 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.
  7. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2010. "The impact of the initial condition on robust tests for a linear trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 292-302, 07.
  8. 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.
  9. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
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