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Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics

Author

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  • Harvey, David I.
  • Leybourne, Stephen J.
  • Taylor, A.M. Robert

Abstract

Trend breaks appear to be prevalent in macroeconomic time series, and unit root tests therefore need to make allowance for these if they are to avoid the serious effects that unmodelled trend breaks have on power. Carrion-i-Silvestre et al. (2009) propose a pre-test-based approach which delivers near asymptotically efficient unit root inference both when breaks do not occur and where multiple breaks occur, provided the break magnitudes are fixed. Unfortunately, however, the fixed magnitude trend break asymptotic theory does not predict well the finite sample power functions of these tests, and power can be very low for the magnitudes of trend breaks typically observed in practice. In response to this problem we propose a unit root test that allows for multiple breaks in trend, obtained by taking the infimum of the sequence (across all candidate break points in a trimmed range) of local GLS detrended augmented Dickey–Fuller-type statistics. We show that this procedure has power that is robust to the magnitude of any trend breaks, thereby retaining good finite sample power in the presence of plausibly-sized breaks. We also demonstrate that, unlike the OLS detrended infimum tests of Zivot and Andrews (1992), these tests display no tendency to spuriously reject in the limit when fixed magnitude trend breaks occur under the unit root null.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:177:y:2013:i:2:p:265-284
    DOI: 10.1016/j.jeconom.2013.04.012
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    References listed on IDEAS

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    Cited by:

    1. Paraskevi Salamaliki, 2015. "Economic Policy Uncertainty and Economic Activity: A Focus on Infrequent Structural Shifts," Working Paper Series of the Department of Economics, University of Konstanz 2015-08, Department of Economics, University of Konstanz.
    2. Skrobotov, Anton, 2015. "On Trend, Breaks and Initial Condition in Unit Root Testing," Published Papers mak6, Russian Presidential Academy of National Economy and Public Administration.
    3. Charles Yuji Horioka & Akiko Terada-Hagiwara, 2017. "The impact of sex ratios before marriage on household saving in two Asian countries: The competitive saving motive revisited," Review of Economics of the Household, Springer, vol. 15(3), pages 739-757, September.
    4. Vicente Esteve & Manuel Navarro-Ibáñez & María A. Prats, 2013. "The present value model of US stock prices revisited: long-run evidence with structural breaks, 1871-2010," Working Papers 04/13, Instituto Universitario de Análisis Económico y Social.
    5. David Harvey & Stephen Leybourne, "undated". "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Discussion Papers 14/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    6. Ana Lourdes Morones Carrillo, 2016. "Crecimiento económico en México: restricción por la balanza de pagos," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 39-58, May.
    7. Liddle, Brantley & Messinis, George, 2015. "Revisiting sulfur Kuznets curves with endogenous breaks modeling: Substantial evidence of inverted-Us/Vs for individual OECD countries," Economic Modelling, Elsevier, vol. 49(C), pages 278-285.
    8. Brantley Liddle & George Messinis, 2018. "Revisiting carbon Kuznets curves with endogenous breaks modeling: evidence of decoupling and saturation (but few inverted-Us) for individual OECD countries," Empirical Economics, Springer, vol. 54(2), pages 783-798, March.
    9. Charles Yuji Horioka & Akiko Terada-Hagiwara, 2016. "The Impact of Pre-marital Sex Ratios on Household Saving in Two Asian Countries: The Competitive Saving Motive Revisited," ISER Discussion Paper 0975, Institute of Social and Economic Research, Osaka University.
    10. Harvey, David I. & Leybourne, Stephen J., 2015. "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 184(2), pages 262-279.
    11. repec:kap:iecepo:v:14:y:2017:i:4:d:10.1007_s10368-016-0355-1 is not listed on IDEAS
    12. Harvey, David I. & Leybourne, Stephen J., 2016. "Improving the length of confidence sets for the date of a break in level and trend when the order of integration is unknown," Economics Letters, Elsevier, vol. 145(C), pages 239-245.
    13. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    14. De Vita, Glauco & Trachanas, Emmanouil, 2016. "‘Nonlinear causality between crude oil price and exchange rate: A comparative study of China and India’ — A failed replication (negative Type 1 and Type 2)," Energy Economics, Elsevier, vol. 56(C), pages 150-160.
    15. repec:gam:jecnmx:v:5:y:2017:i:2:p:17-:d:95932 is not listed on IDEAS
    16. Neil Kellard & Denise Osborn & Jerry Coakley & Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2015. "Testing for Unit Roots Under Multiple Possible Trend Breaks and Non-Stationary Volatility Using Bootstrap Minimum Dickey–Fuller Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 603-629, September.
    17. repec:eee:ecosta:v:4:y:2017:i:c:p:70-90 is not listed on IDEAS
    18. Eléazar Zerbo, 2015. "What determines the long-run growth in Sub-Saharan Africa? Exploring the role of energy, trade openness and financial development in six countries," Working Papers hal-01238524, HAL.

    More about this item

    Keywords

    Unit root test; Multiple breaks in trend; Minimum Dickey–Fuller test; Local GLS detrending;

    JEL classification:

    • 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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