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Local Structural Trend Break in Stationarity Testing

  • Anton Skrobotov

    (Gaidar Institute for Economic Policy)

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    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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    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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    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. 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.
    3. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    4. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
    5. 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.
    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. "Unit root testing under a local break in trend," Discussion Papers 10/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    8. 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.
    9. 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.
    10. Pierre Perron & Tomoyoshi Yabu, 2005. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-026, Boston University - Department of Economics.
    11. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
    12. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(04), pages 995-1029, August.
    13. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
    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. 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.
    16. Anton Skrobotov, 2012. "Trend and initial condition in stationarity tests: the asymptotic analysis," Working Papers 0048, Gaidar Institute for Economic Policy, revised 2013.
    17. 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.
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