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Seasonal Nonstationarity and Near-Nonstationarity


  • Eric Ghysels
  • Denise R. Osborn
  • Paulo M. M. Rodrigues


This paper presents a detailed discussion of the characteristics of seasonal integrated and near integrated processes, as well as the asymptotic properties of seasonal unit root tests. More specifically, the characteristics of a seasonal random walk and a more general seasonal integrated ARMA process are analysed. Also the implications of modelling nonstationary stochastic season-ality as deterministic are highlighted. A further observation made includes the asymptotic distributions and power functions of several seasonal unit root tests. Dans cet article, nous étudions les propriétés des processsus avec racines unitaires saisonnières et avec racines quasi-unitaires. Nous traitons le cas des marchés aléatoires ainsi que les processus plus généraux et analysons les distributions des estimateurs et les fonctions de puissances de plusieurs tests.

Suggested Citation

  • Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO.
  • Handle: RePEc:cir:cirwor:99s-05

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    References listed on IDEAS

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    Cited by:

    1. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, March.
    2. Patrice Roussel & Michel Tremblay, 1999. "Modelling the Role of Organizational Justice: Effects on Satisfaction and Unionization Propensity of Canadian Managers," CIRANO Working Papers 99s-16, CIRANO.
    3. Jérôme Foulon & Paul Lanoie & Benoit Laplante, 1999. "Incentives for Pollution Control: Regulation or (and?) Information," CIRANO Working Papers 99s-11, CIRANO.
    4. Artur C. B. da Silva Lopes & Antonio Montanes, 2005. "The Behavior Of Hegy Tests For Quarterly Time Series With Seasonal Mean Shifts," Econometric Reviews, Taylor & Francis Journals, vol. 24(1), pages 83-108.
    5. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-533, May.
    6. John W. Galbraith, 1999. "Content Horizons For Forecasts Of Economic Time Series," Departmental Working Papers 1999-01, McGill University, Department of Economics.
    7. Psaradakis, Zacharias, 2000. "Bootstrap tests for unit roots in seasonal autoregressive models," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 389-395, December.

    More about this item


    Deterministic/stochastic seasonality; seasonal unit roots; Saisonnalité déterministique et stochastique; racines unitaires saisonnières;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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