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Testing for Unit Roots in Semi-Annual Data

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  • Sandra G. Feltham
  • David E.A. Giles

Abstract

We consider the problem of testing for unit roots at the zero and seasonal frequencies in time-series data which are recorded semi-annually. The proposed methodology follows that of Hylleberg et al. (1990) and Beaulieu and Miron (1993) for quarterly and monthly data respectively. The non-standard asymptotic distributions for the single and joint tests are derived, and various percentiles of the finite-sample distributions are tabulated. Monte Carlo simulation is used to investigate the powers of the tests, and we illustrate their application to several semi-annual economic time-series.

Suggested Citation

  • Sandra G. Feltham & David E.A. Giles, 1999. "Testing for Unit Roots in Semi-Annual Data," Econometrics Working Papers 9912, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:9912
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp9912.pdf
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    References listed on IDEAS

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    1. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    3. Osborn, Denise R, et al, 1988. "Seasonality and the Order of Integration for Consumption," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 361-377, November.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Robert M. Kunst, 1997. "Testing For Cyclical Non‐Stationarity In Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(2), pages 123-135, March.
    6. Smith, Richard J. & Taylor, A. M. Robert, 1998. "Additional critical values and asymptotic representations for seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 85(2), pages 269-288, August.
    7. Philip Hans Franses & Bart Hobijn, 1997. "Critical values for unit root tests in seasonal time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(1), pages 25-48.
    8. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
    9. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 221-241.
    12. Dolado, Juan J & Jenkinson, Tim & Sosvilla-Rivero, Simon, 1990. "Cointegration and Unit Roots," Journal of Economic Surveys, Wiley Blackwell, vol. 4(3), pages 249-273.
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    Cited by:

    1. Olivier Darné & Claude Diebolt, 2002. "A Note on Seasonal Unit Root Tests," Quality & Quantity: International Journal of Methodology, Springer, vol. 36(3), pages 305-310, August.

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    More about this item

    Keywords

    Unit roots; non-stationary data; seasonality; semi-annual data;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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