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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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    7. 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.
    8. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    9. Mills, Terence C & Crafts, N F R, 2000. "After the Golden Age: A Long-Run Perspective on Growth Rates That Speeded Up, Slowed Down and Still Differ," Manchester School, University of Manchester, vol. 68(1), pages 68-91, January.
    10. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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    Citations

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    Cited by:

    1. Terence Mills & Kerry Patterson, 2013. "Carmichael's Arctan Trend: Precursor of Smooth Transition Functions," Economics & Management Discussion Papers em-dp2013-06, Henley Business School, Reading University.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Hepsag, Aycan, 2017. "New unit root tests with two smooth breaks and nonlinear adjustment," MPRA Paper 83353, University Library of Munich, Germany.
    14. Terence C. Mills, 2012. "Semi-parametric modelling of temperature records," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 361-383, May.
    15. Antonio E. Noriega & Cid Alonso Rodríguez-Pérez, 2011. "Stationarity, structural breaks, and economic growth in Mexico: 1895-2008," Working Papers 2011-11, Banco de México.

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