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Unit roots and double smooth transitions

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  • David Harvey
  • Terence Mills

Abstract

Techniques for testing the null hypothesis of difference stationarity against stationarity around some deterministic function have received much attention. In particular, unit root tests where the alternative is stationarity around a smooth transition in a linear trend have recently been proposed to permit the possibility of non-instantaneous structural change. In this paper we develop tests extending such an approach in order to admit more than one structural change. The analysis is motivated by time series that appear to undergo two smooth transitions in the linear trend, and the application of the new tests to two such series (average global temperature and US consumer prices) highlights the benefits of this double transition extension.

Suggested Citation

  • David Harvey & Terence Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 675-683.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:5:p:675-683
    DOI: 10.1080/02664760120098739
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    References listed on IDEAS

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    Cited by:

    1. He, Changli & Sandberg, Rickard, 2005. "Dickey-Fuller Type of Tests against Nonlinear Dynamic Models," SSE/EFI Working Paper Series in Economics and Finance 580, Stockholm School of Economics.
    2. Rickard Sandberg, 2018. "Unit Root Testing in Multiple Smooth Break Models with Nonlinear Dynamics," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 942-952, November.
    3. Hepsag, Aycan, 2017. "New unit root tests with two smooth breaks and nonlinear adjustment," MPRA Paper 83353, University Library of Munich, Germany.
    4. Robert Sollis, 2005. "Evidence on purchasing power parity from univariate models: the case of smooth transition trend‐stationarity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 79-98, January.
    5. Chen, Shyh-Wei & Wu, An-Chi, 2018. "Is there a bubble component in government debt? New international evidence," International Review of Economics & Finance, Elsevier, vol. 58(C), pages 467-486.
    6. Saumitra N. Bhaduri & Ashwin Andrew Samuel, 2009. "International Equity Market Integration," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 8(1), pages 45-66, April.
    7. Changli He & Rickard Sandberg, 2006. "Dickey–Fuller Type of Tests against Nonlinear Dynamic Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 835-861, December.
    8. Xie, Zixiong & Chen, Shyh-Wei & Wu, An-Chi, 2019. "Asymmetric adjustment, non-linearity and housing price bubbles: New international evidence," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    9. Kim, Dukpa & Oka, Tatsushi & Estrada, Francisco & Perron, Pierre, 2020. "Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures," Journal of Econometrics, Elsevier, vol. 214(1), pages 130-152.
    10. Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR model – wavelet improvements under GARCH distortion," Working Paper Series in Economics and Institutions of Innovation 184, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    11. Chen, Shyh-Wei & Xie, Zixiong, 2017. "Asymmetric adjustment and smooth breaks in dividend yields: Evidence from international stock markets," International Review of Economics & Finance, Elsevier, vol. 48(C), pages 339-354.
    12. Holt, Matthew T. & Teräsvirta, Timo, 2020. "Global hemispheric temperatures and co-shifting: A vector shifting-mean autoregressive analysis," Journal of Econometrics, Elsevier, vol. 214(1), pages 198-215.
    13. Francisco Estrada & Pierre Perron, "undated". "Detection and attribution of climate change through econometric methods," Boston University - Department of Economics - Working Papers Series 2013-015, Boston University - Department of Economics.
    14. Richard S. J. Tol & Francisco Estrada & Carlos Gay-García, 2012. "The persistence of shocks in GDP and the estimation of the potential economic costs of climate change," Working Paper Series 4312, Department of Economics, University of Sussex Business School.
    15. Paraskevi Salamaliki & Ioannis Venetis, 2014. "Smooth transition trends and labor force participation rates in the United States," Empirical Economics, Springer, vol. 46(2), pages 629-652, March.
    16. Xie, Zixiong & Chen, Shyh-Wei & Hsieh, Chun-Kuei, 2021. "Facing up to the polysemy of purchasing power parity: New international evidence," Economic Modelling, Elsevier, vol. 98(C), pages 247-265.
    17. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    18. He, Changli & Sandberg, Rickard, 2005. "Testing for Unit Roots in Nonlinear Dynamic Heterogeneous Panels," SSE/EFI Working Paper Series in Economics and Finance 582, Stockholm School of Economics.
    19. Terence C. Mills, 2012. "Semi-parametric modelling of temperature records," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 361-383, May.
    20. Dukpa Kim & Tatsushi Oka & Francisco Estrada & Pierre Perron, 2017. "Inference Related to Common Breaks in a Multivariate System with Joined Segmented Trends with Applications to Global and Hemispheric Temperatures," Boston University - Department of Economics - Working Papers Series WP2017-003, Boston University - Department of Economics.
    21. Robert Sollis, 2005. "Evidence on purchasing power parity from univariate models: the case of smooth transition trend-stationarity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 79-98.
    22. Terence Mills & Kerry Patterson, 2013. "Carmichael's Arctan Trend: Precursor of Smooth Transition Functions," Economics Discussion Papers em-dp2013-06, Department of Economics, University of Reading.
    23. Terence C. Mills & David I. Harvey, 2003. "Modelling trends in central England temperatures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 35-47.
    24. Terence C. Mills, 2007. "Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 83-94, January.
    25. 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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