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Seasonality Tests

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  • Busetti, Fabio
  • Harvey, Andrew

Abstract

This article modifies and extends the test against nonstationary stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for structural breaks, or by the inclusion of regressors with nonseasonal unit roots. A parametric version of the test is proposed, and its performance is compared with that of the nonparametric test using Monte Carlo experiments. A test that allows for breaks in the seasonal pattern is then derived. It is shown that its asymptotic distribution is independent of the break point, and its use is illustrated with a series on U.K. marriages. A general test against any form of permanent seasonality, deterministic or stochastic, is suggested and compared with a Wald test for the significance of fixed seasonal dummies. It is noted that tests constructed in a similar way can be used to detect trading-day effects. An appealing feature of the proposed test statistics is that under the null hypothesis, they all have asymptotic distributions belonging to the Cramer-von Mises family.

Suggested Citation

  • Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-436, July.
    • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:3:p:420-36
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    Citations

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    Cited by:

    1. El Montasser, Ghassen, 2014. "The seasonal KPSS Test: some extensions and further results," MPRA Paper 54920, University Library of Munich, Germany.
    2. Proietti, Tommaso & Pedregal, Diego J., 2023. "Seasonality in High Frequency Time Series," Econometrics and Statistics, Elsevier, vol. 27(C), pages 62-82.
    3. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    4. Tommaso Proietti & Eric Hillebrand, 2017. "Seasonal changes in central England temperatures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 769-791, June.
    5. Tommaso Proietti & Stefano Grassi, 2015. "Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search," Empirical Economics, Springer, vol. 48(3), pages 983-1011, May.
    6. Irma Hindrayanto & John A.D. Aston & Siem Jan Koopman & Marius Ooms, 2013. "Modelling trigonometric seasonal components for monthly economic time series," Applied Economics, Taylor & Francis Journals, vol. 45(21), pages 3024-3034, July.
    7. Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.
    8. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438, May.
    9. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    10. Tommaso, Proietti & Stefano, Grassi, 2010. "Bayesian stochastic model specification search for seasonal and calendar effects," MPRA Paper 27305, University Library of Munich, Germany.
    11. E. Andersson & D. Bock & M. Frisen, 2006. "Some statistical aspects of methods for detection of turning points in business cycles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 257-278.
    12. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
    13. El Montasser, Ghassen, 2012. "The seasonal KPSS Test: some extensions and further results," MPRA Paper 45110, University Library of Munich, Germany, revised 04 Mar 2014.
    14. Tommaso Proietti & Cecilia Frale, 2011. "New proposals for the quantification of qualitative survey data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(4), pages 393-408, July.
    15. Ghassen El Montasser, 2015. "The Seasonal KPSS Test: Examining Possible Applications with Monthly Data and Additional Deterministic Terms," Econometrics, MDPI, vol. 3(2), pages 1-16, May.
    16. Webel, Karsten, 2016. "A data-driven selection of an appropriate seasonal adjustment approach," Discussion Papers 07/2016, Deutsche Bundesbank.
    17. McElroy Tucker, 2021. "A Diagnostic for Seasonality Based Upon Polynomial Roots of ARMA Models," Journal of Official Statistics, Sciendo, vol. 37(2), pages 367-394, June.
    18. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.
    19. Apergis, Nicholas & Lau, Marco Chi Keung, 2015. "Structural breaks and electricity prices: Further evidence on the role of climate policy uncertainties in the Australian electricity market," Energy Economics, Elsevier, vol. 52(PA), pages 176-182.

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