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Testing for (Common) Stochastic Trends in the Presence of Structural Breaks


  • Busetti, Fabio


This paper considers the problem of testing for the presence of stochastic trends in multivariate time series with structural breaks. The breakpoints are assumed to be known. The testing framework is the multivariate locally best invariant test and the common trend test of Nyblom and Harvey (2000). The asymptotic distributions of the test statistics are derived under a specification of the deterministic component which allows for structural breaks. Asymptotic critical values are provided for the case of a single breakpoint. A modified statistic is then proposed, the asymptotic distribution of which is independent of the breakpoint location and belongs to the Cramer-von Mises family. This modification is particularly advantageous in the case of multiple breakpoints. It is also shown that the asymptotic distributions of the test statistics are unchanged when seasonal dummy variables and/or weakly dependent exogenous regressors are included. Finally, as an example, the tests are applied to UK macroeconomic data and to data on road casualties in Great Britain. Copyright © 2002 by John Wiley & Sons, Ltd.

Suggested Citation

  • Busetti, Fabio, 2002. "Testing for (Common) Stochastic Trends in the Presence of Structural Breaks," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(2), pages 81-105, March.
  • Handle: RePEc:jof:jforec:v:21:y:2002:i:2:p:81-105

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    References listed on IDEAS

    1. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    2. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    3. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    4. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    5. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    6. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    7. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. " On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-735, June.
    8. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    9. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    10. Bollerslev, Tim & Domowitz, Ian, 1993. " Trading Patterns and Prices in the Interbank Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 48(4), pages 1421-1443, September.
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    Cited by:

    1. Joseph P. Byrne & Roger Perman, 2006. "Unit Roots and Structural Breaks: A Survey of the Literature," Working Papers 2006_10, Business School - Economics, University of Glasgow.
    2. Sven Schreiber, 2012. "Estimating the natural rate of unemployment in euro-area countries with co-integrated systems," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1315-1335, April.
    3. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Testing the Null of Cointegration with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(5), pages 623-646, October.
    4. Banerjee, Anindya & Carrion-i-Silvestre, Josep Lluís, 2006. "Cointegration in panel data with breaks and cross-section dependence," Working Paper Series 591, European Central Bank.

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