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Local Structural Trend Break in Stationarity Testing


  • Anton Skrobotov

    (Gaidar Institute for Economic Policy)


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).

Suggested Citation

  • Anton Skrobotov, 2013. "Local Structural Trend Break in Stationarity Testing," Working Papers 0074, Gaidar Institute for Economic Policy, revised 2013.
  • Handle: RePEc:gai:wpaper:0074

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    References listed on IDEAS

    1. Carrion-i-Silvestre, Josep LluĂ­s & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1754-1792, December.
    2. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    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. 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, March.
    5. 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.
    6. 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.
    7. Cavaliere, Giuseppe & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2011. "Testing For Unit Roots In The Presence Of A Possible Break In Trend And Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 27(05), pages 957-991, October.
    8. 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.
    9. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    10. 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, March.
    11. 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.
    12. 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.
    13. 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.
    14. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
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    More about this item


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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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