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A sequential approach to testing seasonal unit roots in high frequency data

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  • Paulo Rodrigues
  • Philip Hans Franses

Abstract

In this paper we introduce a sequential seasonal unit root testing approach which explicitly addresses its application to high frequency data. The main idea is to see which unit roots at higher frequency data can also be found in temporally aggregated data. We illustrate our procedure to the analysis of monthly data, and we find, upon analysing the aggregated quarterly data, that a smaller amount of test statistics can sometimes be considered. Monte Carlo simulation and empirical illustrations emphasize the practical relevance of our method.

Suggested Citation

  • Paulo Rodrigues & Philip Hans Franses, 2005. "A sequential approach to testing seasonal unit roots in high frequency data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(6), pages 555-569.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:6:p:555-569
    DOI: 10.1080/02664760500078912
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    References listed on IDEAS

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    1. Franses, Philip Hans, 1991. "Seasonality, non-stationarity and the forecasting of monthly time series," International Journal of Forecasting, Elsevier, vol. 7(2), pages 199-208, August.
    2. Robert Taylor, "undated". "Additional Critical Values and Asymptotic Representations for Monthly Seasonal Unit Root Tests," Discussion Papers 96/13, Department of Economics, University of York.
    3. 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.
    4. Smith, Richard J. & Taylor, A.M. Robert & del Barrio Castro, Tomas, 2009. "Regression-Based Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 25(02), pages 527-560, April.
    5. A. M. Robert Taylor, 1998. "Testing for Unit Roots in Monthly Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 349-368, May.
    6. Franses, Philip Hans, 1996. "Recent Advances in Modelling Seasonality," Journal of Economic Surveys, Wiley Blackwell, vol. 10(3), pages 299-345, September.
    7. 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.
    8. Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests with Recursive Mean Adjustment," Discussion Papers 99-11, Department of Economics, University of Birmingham.
    9. 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.
    10. Paulo Rodrigues & Denise Osborn, 1999. "Performance of seasonal unit root tests for monthly data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 985-1004.
    11. 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.
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    Cited by:

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    2. Jani Beko & Timotej Jagric, 2009. "Demand models for direct mail and periodicals delivery services: results for a transition economy," Applied Economics, Taylor & Francis Journals, vol. 43(9), pages 1125-1138.
    3. Gabriel Pons Rotger, 2004. "Seasonal Unit Root Testing Based on the Temporal Aggregation of Seasonal Cycles," Economics Working Papers 2004-1, Department of Economics and Business Economics, Aarhus University.
    4. Roberto Martínez-Espiñeira, 2007. "An Estimation of Residential Water Demand Using Co-Integration and Error Correction Techniques," Journal of Applied Economics, Taylor & Francis Journals, vol. 10(1), pages 161-184, May.
    5. Andres Silva & Senarath Dharmasena, 2016. "Considering seasonal unit root in a demand system: an empirical approach," Empirical Economics, Springer, vol. 51(4), pages 1443-1463, December.
    6. Gabriel Pons, 2006. "Testing Monthly Seasonal Unit Roots With Monthly and Quarterly Information," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 191-209, March.
    7. Ridderstaat, Jorge & Oduber, Marck & Croes, Robertico & Nijkamp, Peter & Martens, Pim, 2014. "Impacts of seasonal patterns of climate on recurrent fluctuations in tourism demand: Evidence from Aruba," Tourism Management, Elsevier, vol. 41(C), pages 245-256.

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    Keywords

    Seasonal unit roots; temporal aggregation;

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