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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)

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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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Publisher 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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April. [Downloadable!]
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  2. 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.
    Other versions:
  3. 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.
  4. Nyblom, Jukka, 2001. "Invariant Tests for Covariance Structures in Multivariate Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 294-315, February. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  6. 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.
  7. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge. [Downloadable!]
  2. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge. [Downloadable!]
    Other versions:
  3. 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). [Downloadable!]
  4. Busetti, F. & Harvey, A., 2008. "When is a copula constant? A test for changing relationships," Cambridge Working Papers in Economics 0841, Faculty of Economics, University of Cambridge. [Downloadable!]
  5. 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. [Downloadable!]
    Other versions:
  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. [Downloadable!]
    Other versions:
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