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Structural Change and the Order of Integration in Univariate Time Series

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  • Luis A. Gil-Alana

    (Facultad de Ciencias Economicas, Universidad de Navarra, Edificio Biblioteca, Entrada Este, 31080 Pamplona, Spain)

Abstract

In this article I investigate whether the presence of structural breaks affects inference on the order of integration in univariate time series. For this purpose, we make use of a version of the tests of Robinson (1994) which allows us to test unit and fractional roots in the presence of deterministic changes. Several Monte Carlo experiments conducted across the paper show that the tests perform relatively well in the presence of both mean and slope breaks. The tests are applied to annual data on German real GDP, the results showing that the series may be well described in terms of a fractional model with a structural slope break due to World War II.

Suggested Citation

  • Luis A. Gil-Alana, 2004. "Structural Change and the Order of Integration in Univariate Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 23(3), pages 239-254, April.
    • Handle: RePEc:kap:compec:v:23:y:2004:i:3:p:239-254
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    1. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    2. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    3. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    4. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    5. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
    6. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
    7. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-250, July.
    8. Gil-Alana, Luis A., 2001. "A fractionally integrated model with a mean shift for the US and the UK real oil prices," Economic Modelling, Elsevier, vol. 18(4), pages 643-658, December.
    9. L. A. Gil‐Alana, 2001. "Testing Stochastic Cycles in Macroeconomic Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 411-430, July.
    10. Hidalgo, Javier & Robinson, Peter M., 1996. "Testing for structural change in a long-memory environment," Journal of Econometrics, Elsevier, vol. 70(1), pages 159-174, January.
    11. Clive W.J. Granger & Namwon Hyung, 2013. "Occasional Structural Breaks and Long Memory," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 739-764, November.
    12. Gil-Alana, Luis A., 1999. "Testing fractional integration with monthly data," Economic Modelling, Elsevier, vol. 16(4), pages 613-629, December.
    13. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    14. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    15. Vadim Teverovsky & Murad Taqqu, 1997. "Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(3), pages 279-304, May.
    16. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
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    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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