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Tests for Stationarity in Series with Endogenously Determined Structural Change

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  • David I. Harvey
  • Terence C. Mills

Abstract

We consider tests of the null hypothesis of stationarity against a unit root alternative, when the series is subject to structural change at an unknown point in time. Three extant tests are reviewed which allow for an endogenously determined instantaneous structural break, and a related fourth procedure is introduced. We further propose tests which permit the structural change to be gradual rather than instantaneous, allowing the null hypothesis to be stationarity about a smooth transition in linear trend. The size and power properties of the tests are investigated, and the tests are applied to four economic time series.

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  • David I. Harvey & Terence C. Mills, 2004. "Tests for Stationarity in Series with Endogenously Determined Structural Change," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(5), pages 863-894, December.
    • Handle: RePEc:bla:obuest:v:66:y:2004:i:5:p:863-894
    DOI: 10.1111/j.1468-0084.2004.105_1.x
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    4. Fabio Busetti & Andrew Harvey, 2001. "Testing for the Presence of a Random Walk in Series with Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 127-150, March.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    7. David I. Harvey & Stephen J. Leybourne & Paul Newbold, 2001. "Innovational Outlier Unit Root Tests With an Endogenously Determined Break in Level," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 559-575, December.
    8. 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.
    9. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
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    12. 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.
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    14. Perron, P, 1993. "Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]," Econometrica, Econometric Society, vol. 61(1), pages 248-249, January.
    15. Junsoo Lee & Mark Strazicich, 2001. "Testing the null of stationarity in the presence of a structural break," Applied Economics Letters, Taylor & Francis Journals, vol. 8(6), pages 377-382.
    16. 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.
    17. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 2001. "Innovational Outlier Unit Root Tests with an Endogenously Determined Break in Level," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 559-575, December.
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    Cited by:

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    3. Brittle, Shane, 2009. "Ricardian Equivalence and the Efficacy of Fiscal Policy in Australia," Economics Working Papers wp09-10, School of Economics, University of Wollongong, NSW, Australia.
    4. Ivan D. Trofimov, 2019. "Stability of Labour Shares: Evidence from OECD Economies," South-Eastern Europe Journal of Economics, Association of Economic Universities of South and Eastern Europe and the Black Sea Region, vol. 17(1), pages 57-89.
    5. Chun‐Yu Ho & Dan Li, 2008. "Rising regional inequality in China: Policy regimes and structural changes," Papers in Regional Science, Wiley Blackwell, vol. 87(2), pages 245-259, June.
    6. Peter Sephton, 2017. "Finite Sample Critical Values of the Generalized KPSS Stationarity Test," Computational Economics, Springer;Society for Computational Economics, vol. 50(1), pages 161-172, June.
    7. D., Ivan, 2017. "Stability of the labour shares: evidence from OECD economies," MPRA Paper 79822, University Library of Munich, Germany.
    8. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
    9. María Presno & Manuel Landajo, 2010. "Computation of limiting distributions in stationarity testing with a generic trend," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 165-183, March.
    10. Manuel Landajo & María José Presno, 2010. "Stationarity testing under nonlinear models. Some asymptotic results," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 392-405, September.
    11. Alper Kara & Dilem Yildirim & G. Ipek Tunc, 2023. "Market efficiency in non-renewable resource markets: evidence from stationarity tests with structural changes," Mineral Economics, Springer;Raw Materials Group (RMG);Luleå University of Technology, vol. 36(2), pages 279-290, June.
    12. Alper Kara & Dilem Yıldırım & Gül İpek Tunç, 2021. "Market Efficiency In Non-Renewable Resource Markets: Evidence From Stationarity Tests With Structural Changes," ERC Working Papers 2103, ERC - Economic Research Center, Middle East Technical University, revised Apr 2021.
    13. Noriega Antonio E. & Rodríguez-Pérez Cid Alonso, 2011. "Stationarity, structural breaks, and economic growth in Mexico: 1895-2008," Working Papers 2011-11, Banco de México.

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