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Testing against smooth stochastic trends

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Author Info

  • 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.

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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 16 (2001)
Issue (Month): 3 ()
Pages: 415-429

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Handle: RePEc:jae:japmet:v:16:y:2001:i:3:p:415-429

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References

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  1. Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 253-64, July.
  2. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  3. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
  4. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
  5. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
  6. Nyblom, Jukka, 2001. "Invariant Tests for Covariance Structures in Multivariate Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 294-315, February.
  7. Nyblom, Jukka & Harvey, Andrew, 1999. "Tests of Common Stochastic Trends," Cambridge Working Papers in Economics 9902, Faculty of Economics, University of Cambridge.
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Citations

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Cited by:
  1. 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, School of Economics and Management, University of Aarhus.
  2. 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.
  3. Siem Jan Koopman & André Lucas & Marius Ooms & Kees van Montfort & Victor van der Geest, 2007. "Estimating Systematic Continuous-time Trends in Recidivism using a Non-Gaussian Panel Data Model," Tinbergen Institute Discussion Papers 07-027/4, Tinbergen Institute.
  4. Siem Jan Koopman & André Lucas & Marius Ooms & Kees van Montfort & Victor van der Geest, 2007. "Estimating Systematic Continuous-time Trends in Recidivism using a Non-Gaussian Panel Data Model," Tinbergen Institute Discussion Papers 07-027/4, Tinbergen Institute.
  5. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge.
  6. C.S. Bos & S.J. Koopman & M. Ooms, 2007. "Long Memory Modelling of Inflation with Stochastic Variance and Structural Breaks," Tinbergen Institute Discussion Papers 07-099/4, Tinbergen Institute.
  7. Suncica Vujic & Siem Jan Koopman & Jacques J. F. Commandeur, 2012. "Economic Trends and Cycles in Crime: A Study for England and Wales," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 232(6), pages 652-677, November.
  8. Guilhem Bentoglio & Jacky Fayolle & Matthieu Lemoine, 2002. "Unity and Plurality of the European Cycle," Documents de Travail de l'OFCE 2002-03, Observatoire Francais des Conjonctures Economiques (OFCE).
  9. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
  10. repec:spo:wpecon:info:hdl:2441/2133 is not listed on IDEAS
  11. Christopher Klein & Shea Slonaker, 2010. "Chart Turnover and Sales in the Recorded Music Industry: 1990–2005," Review of Industrial Organization, Springer, vol. 36(4), pages 351-372, June.
  12. Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 106-131, Winter.

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