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Testing against smooth stochastic trends

Author

Listed:
  • Jukka Nyblom

    (Department of Statistics, University of Joensuu, PO Box 111, FIN-80101 Joensuu, Finland)

  • Andrew Harvey

    (Faculty of Economics and Politics, University of Cambridge, Sidgwick Avenue, Cambridge, CB3 9DD, UK)

Abstract
A trend estimated from an unobserved components model tends to be smoother when it is modelled as an integrated random walk rather than a random walk with drift. This article derives a test of the null hypothesis that the trend is deterministic against the alternative that it is an integrated random walk. It is assumed that the other component in the model is normally distributed white noise. Critical values are tabulated, the asymptotic distribution is derived and the performance of the test is compared with the test against a trend specified as a random walk with drift. The test is extended to allow for serially correlated and evolving seasonal components. When there is a stationary process containing a single autoregressive unit root close to one, a bounds test can be applied. In the case of a first-order autoregressive disturbance, it is shown that a consistent test can still be obtained by carrying out estimation of the nuisance parameters under the null hypothesis. The overall conclusion is that the most effective test against an integrated random walk is a parametric one based on the random walk plus drift test statistic, constructed from innovations, with the nuisance parameters estimated in the unrestricted model. Copyright © 2001 John Wiley & Sons, Ltd.

Suggested Citation

  • Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
    • Handle: RePEc:jae:japmet:v:16:y:2001:i:3:p:415-429
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    File URL: http://qed.econ.queensu.ca:80/jae/2001-v16.3/
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    References listed on IDEAS

    as
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    4. Guilhem Bentoglio & Jacky Fayolle & Matthieu Lemoine, 2002. "Unity and Plurality of the European Cycle," Working Papers hal-03458584, HAL.
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    8. Xiaoshan Chen & Terence Mills, 2012. "Measuring the Euro area output gap using a multivariate unobserved components model containing phase shifts," Empirical Economics, Springer, vol. 43(2), pages 671-692, October.
    9. Vujić Sunčica & Koopman Siem Jan & Commandeur J.F., 2012. "Economic Trends and Cycles in Crime: A Study for England and Wales," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 232(6), pages 652-677, December.
    10. Charles S. Bos & Siem Jan Koopman & Marius Ooms, 2007. "Long memory modelling of inflation with stochastic variance and structural breaks," CREATES Research Papers 2007-44, Department of Economics and Business Economics, Aarhus University.
    11. Siem Jan Koopman & Marius Ooms & André Lucas & Kees van Montfort & Victor Van Der Geest, 2008. "Estimating systematic continuous‐time trends in recidivism using a non‐Gaussian panel data model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 104-130, February.
    12. Xiaoyi Mu and Haichun Ye, 2015. "Small Trends and Big Cycles in Crude Oil Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    13. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge.
    14. Juan G Brida & Bibiana Lanzilotta & Lucia I Rosich, 2021. "On the empirical relations between producers expectations and economic growth," Economics Bulletin, AccessEcon, vol. 41(3), pages 1970-1982.
    15. Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 106-131, Winter.
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    17. Ferrara, L. & Koopman, S J., 2010. "Common business and housing market cycles in the Euro area from a multivariate decomposition," Working papers 275, Banque de France.
    18. Xiaoshan Chen & Ronald MacDonald, 2010. "Revisiting the Dollar-Euro Permanent Equilibrium Exchange Rate: Evidence from Multivariate Unobserved Components Models," Working Papers 2010_16, Business School - Economics, University of Glasgow.
    19. Fabio Busetti & Andrew Harvey, 2010. "Tests of strict stationarity based on quantile indicators," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 435-450, November.
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