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Local Structural Trend Break in Stationarity Testing

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  • Anton Skrobotov

    (Gaidar Institute for Economic Policy)

Abstract

In a recently publicized study, Harvey et al. (2012) investigated procedures for unit root testing employing break detection methods under local break in trend. We apply this methodology to analyze asymptotic and unite sample behavior of procedures under local break to test the stationarity null hypothesis local to unit root, against alternative hypothesis about the pres- ence of a unit root. We extend the GLS-based stationarity test proposed by Harris et al. (2007) to the case of structural break and obtain asymptotic properties under local trend break. Two procedures are considered. The first procedure uses a with-break stationarity test, but with adaptive critical values. The second procedure utilizes the intersection of rejection testing strategy containing tests with and without a break. Application of these approaches help to prevent serious size distortions for small break magnitude that are otherwise undetectable. Additionally, in a similar approach as Harvey et al. (2013) and Busetti and Harvey (2001), we propose a test based on minimizing the sequence of GLS-based stationarity test statistics over all possible break dates. This infimum-test in contrast to Busetti and Harvey (2001) does not require an additional assumption about a faster rate of convergence of break magnitude. Asymptotic and unite sample simulations show that under local to zero behavior of the trend break the asymptotic analysis provides a good approximation of the unite sample behavior of the proposed procedures. Proposed procedures can be used for confirmatory analysis together with tests of Harvey et al. (2012) and Harvey et al. (2013).

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File URL: http://www.iep.ru/files/RePEc/gai/wpaper/0074Skrobotov.pdf
File Function: Revised version, 2013
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Bibliographic Info

Paper provided by Gaidar Institute for Economic Policy in its series Working Papers with number 0074.

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Length: 23 pages
Date of creation: 2013
Date of revision: 2013
Handle: RePEc:gai:wpaper:0074

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Related research

Keywords: Stationarity tests; KPSS tests; local break in trend; size distortions; intersection of rejection decision rule..;

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References

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  1. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
  2. 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.
  3. David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, . "Simple, Robust and Powerful Tests of the Breaking Trend Hypothesis," Discussion Papers 06/11, University of Nottingham, School of Economics.
  4. 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.
  5. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
  6. 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.
  7. Fabio Busetti & Andrew Harvey, 2003. "Further Comments On Stationarity Tests In Series With Structural Breaks At Unknown Points," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 137-140, 03.
  8. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Unit root testing under a local break in trend," Journal of Econometrics, Elsevier, vol. 167(1), pages 140-167.
  9. 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.
  10. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  11. David Harris & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Testing for a unit root in the presence of a possible break in trend," Discussion Papers 07/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  12. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
  13. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
  14. David I. Harvey & Terence C. Mills, 2003. "A Note On Busetti-Harvey Tests For Stationarity In Series With Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 159-164, 03.
  15. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2013. "Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics," Journal of Econometrics, Elsevier, vol. 177(2), pages 265-284.
  16. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
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