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Unit roots and double smooth transitions

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  • David Harvey
  • Terence Mills
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    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.

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    Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 29 (2002)
    Issue (Month): 5 ()
    Pages: 675-683

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    Handle: RePEc:taf:japsta:v:29:y:2002:i:5:p:675-683
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    1. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Universite de Montreal, Departement de sciences economiques.
    2. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
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    4. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
    5. 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.
    6. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
    7. 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.
    8. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    10. Seater, John J, 1993. "World Temperature-Trend Uncertainties and Their Implications for Economic Policy," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 265-77, July.
    11. Michael P. Clements & David F. Hendry, 2001. "Forecasting Non-Stationary Economic Time Series," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531895, June.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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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