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Unit Roots and Asymmetric Smooth Transitions

Author

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  • Robert Sollis
  • Stephen Leybourne
  • Paul Newbold

Abstract

It has been found useful, as an alternative to a difference‐stationary generating model, to consider the possibility of stationarity around a function that permits a smooth transition from one linear trend to another. Previous research has concentrated on functions that are symmetric around the point at which 50% of the transition is completed. Here we permit the possibility of asymmetry in the transition, allowing for example slow entry to and rapid exit from this evolutionary phase. It is shown through simulation and an interesting real data set that this can lead to the detection of further departures from difference stationarity.

Suggested Citation

  • Robert Sollis & Stephen Leybourne & Paul Newbold, 1999. "Unit Roots and Asymmetric Smooth Transitions," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 671-677, November.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:6:p:671-677
    DOI: 10.1111/1467-9892.00165
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    1. Alessandra Canepa & Emilio Zanetti Chini & Huthaifa Alqaralleh, 2020. "Global Cities and Local Housing Market Cycles," The Journal of Real Estate Finance and Economics, Springer, vol. 61(4), pages 671-697, November.
    2. R. Velazquez & A.E. Noriega & L.M. Soria, 2004. "International Evidence on Monetary Neutrality Under Broken Trend Stationary Models," Econometric Society 2004 Latin American Meetings 57, Econometric Society.
    3. 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.
    4. David Harvey & Terence Mills, 2002. "Unit roots and double smooth transitions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 675-683.
    5. Ilias Lekkos & Costas Milas & Theodore Panagiotidis, 2007. "Forecasting interest rate swap spreads using domestic and international risk factors: evidence from linear and non-linear models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(8), pages 601-619.
    6. 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.
    7. Daniel Parra-Amado & Davinson Stev Abril-Salcedo & Luis Fernando Melo-Velandia, 2016. "Impactos de los fenómenos climáticos sobre el precio de los alimentos en Colombia," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República, vol. 34(80), pages 146-158, June.
    8. Lundbergh, Stefan & Terasvirta, Timo, 2006. "A time series model for an exchange rate in a target zone with applications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 579-609.
    9. Neil Foster-McGregor & Robert Stehrer, 2005. "Modelling GDP in CEECs Using Smooth Transitions," wiiw Working Papers 36, The Vienna Institute for International Economic Studies, wiiw.
    10. Emilio Zanetti Chini, 2013. "Generalizing smooth transition autoregressions," CREATES Research Papers 2013-32, Department of Economics and Business Economics, Aarhus University.
    11. Davinson Stev Abril‐Salcedo & Luis Fernando Melo‐Velandia & Daniel Parra‐Amado, 2020. "Nonlinear relationship between the weather phenomenon El niño and Colombian food prices," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 64(4), pages 1059-1086, October.
    12. Noriega, Antonio E. & Soria, Luis M. & Velázquez, Ramón, 2008. "International evidence on stochastic and deterministic monetary neutrality," Economic Modelling, Elsevier, vol. 25(6), pages 1261-1275, November.
    13. Oleg Korenok & Stanislav Radchenko, 2005. "The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications," Econometrics 0508015, University Library of Munich, Germany.
    14. 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.
    15. Nektarios Aslanidis & Susana Iranzo, 2009. "Environment and development: is there a Kuznets curve for CO2 emissions?," Applied Economics, Taylor & Francis Journals, vol. 41(6), pages 803-810.
    16. Vougas, Dimitrios V., 2006. "On unit root testing with smooth transitions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 797-800, November.
    17. Zanetti Chini, Emilio, 2018. "Forecasting dynamically asymmetric fluctuations of the U.S. business cycle," International Journal of Forecasting, Elsevier, vol. 34(4), pages 711-732.
    18. Canepa, Alessandra & Chini, Emilio Zanetti, 2016. "Dynamic asymmetries in house price cycles: A generalized smooth transition model," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 91-103.
    19. 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.
    20. Canepa, Alessandra & Zanetti Chini, Emilio & Alqaralleh, Huthaifa, 2019. "Modelling Housing Market Cycles in Global Cities," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201901, University of Turin.

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