On Seasonal Cycles, Unit Roots, And Mean Shifts

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On Seasonal Cycles, Unit Roots, And Mean Shifts

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Philip Hans Franses
Timothy J. Vogelsang

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Abstract

The interpretation of seasonality in terms of economic behavior depends on the form of the econometric time-series model that allows for a description of seasonality. Popular models often assume either approximate deterministic seasonality (cf. Miron (1996)) or stochastic trend seasonality (cf. Hylleberg (1994)). Inference from an inappropriate model can be shown to be invalid. Since much graphical evidence clearly suggests that seasonal fluctuations are not constant over time, we investigate whether the finding of seasonal unit roots can be due to neglected mean shifts. We provide relevant asymptotic theory and critical values for various test statistics. For a set of real gross domestic product series we find that much evidence for seasonal unit roots tends to disappear when a shift in the seasonal means is allowed. When we incorporate deterministic mean shifts in the deterministic seasonality model, we find that qualitative results on the presence of the so-called seasonal cycle documented in, for example, Miron and Beaulieu (1996) are robust. © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technolog

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Publisher Info
Article provided by MIT Press in its journal The Review of Economics and Statistics.

Volume (Year): 80 (1998)
Issue (Month): 2 (May)
Pages: 231-240
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Handle: RePEc:tpr:restat:v:80:y:1998:i:2:p:231-240

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P.H. Franses & D. Van Dijk, 2001. "The Forecasting Performance of Various Models for Seasonality and Nonlinearity for Quarterly Industrial Production," Econometric Institute Report 222, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Franses, Philip Hans & van Dijk, Dick, 2005. "The forecasting performance of various models for seasonality and nonlinearity for quarterly industrial production," International Journal of Forecasting, Elsevier, vol. 21(1), pages 87-102. [Downloadable!] (restricted)
van Dijk, Dick & Strikholm, Birgit & Teräsvirta, Timo, 2001. "The effects of institutional and technological change and business cycle fluctuations on seasonal patterns in quarterly industrial production series," Working Paper Series in Economics and Finance 0429, Stockholm School of Economics, revised 16 May 2002. [Downloadable!]
Other versions:
- D. Van Dijk & D. Strikholm & T. Terasvirta, 2001. "The effects of institutional and technological change and business cycle fluctiations on seasonal patterns in quarterly industrial production series," Econometric Institute Report 220, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Dijk, D.J.C. van & Strikholm, B. & Terasvirta, T., 2001. "The effects of institutional and technological change and business cycle fluctiations on seasonal patterns in quarterly industrial production series," Econometric Institute Report EI 2001-12 Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Dick van Dijk ¹ & Birgit Strikholm & Timo Teräsvirta, 2003. "The effects of institutional and technological change and business cycle fluctuations on seasonal patterns in quarterly industrial production series," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 79-98, 06. [Downloadable!] (restricted)
Gustavsson, Patrik & Nordström, Jonas, 1999. "The Impact of Seasonal Unit Roots and Vector ARMA Modeling on Forecasting Monthly Tourism Flows," Working Paper Series 150, Trade Union Institute for Economic Research, revised 01 Jul 2000. [Downloadable!]
Artur C. B. da Silva Lopes & Antonio Montañés, 2004. "The Behavior of HEGY Tests for Quarterly Time Series with Seasonal Mean Shifts," Econometrics 0411010, EconWPA. [Downloadable!]
Niels Haldrup & Antonio Montanés & Andreu Sanso, . "Measurement Errors and Outliers in Seasonal Unit Root Testing," Economics Working Papers 2000-8, School of Economics and Management, University of Aarhus. [Downloadable!]
Other versions:
- Niel Haldrup & Antonio MontanŽs & Andreu Sanso, 2000. "Measurement Errors and Outliers in Seasonal Unit Root Testing," University of California at San Diego, Economics Working Paper Series 2000-15, Department of Economics, UC San Diego. [Downloadable!]
- Haldrup, Niels & Montanes, Antonio & Sanso, Andreu, 2005. "Measurement errors and outliers in seasonal unit root testing," Journal of Econometrics, Elsevier, vol. 127(1), pages 103-128, July. [Downloadable!] (restricted)
Gabriel Pons, 2006. "Testing Monthly Seasonal Unit Roots With Monthly and Quarterly Information," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(2), pages 191-209, 03. [Downloadable!] (restricted)
Gabriel Pons Rotger, 2004. "Seasonal Unit Root Testing Based on the Temporal Aggregation of Seasonal Cycles," Economics Working Papers 2004-1, School of Economics and Management, University of Aarhus. [Downloadable!]
Uwe Hassler & Paulo M. M. Rodrigues, 2002. "Seasonal Unit Root Tests under Structural Breaks," Darmstadt Discussion Papers in Economics 113, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
Other versions:
- Uwe Hassler & Paulo M. M. Rodrigues, 2004. "Seasonal Unit Root Tests Under Structural Breaks," Journal of Time Series Analysis, Blackwell Publishing, vol. 25(1), pages 33-53, 01. [Downloadable!] (restricted)
B. da Silva Lopes, Artur C., 2005. "Finite sample effects of pure seasonal mean shifts on Dickey-Fuller tests," MPRA Paper 125, University Library of Munich, Germany, revised May 2006. [Downloadable!]
Harvey, David I. & Leybourne, Stephen J. & Newbold, Paul, 2002. "Seasonal unit root tests with seasonal mean shifts," Economics Letters, Elsevier, vol. 76(2), pages 295-302, July. [Downloadable!] (restricted)
Antonio Montanes & Andreu Sanso, 2001. "The Dickey-Fuller Test Family and Changes in the Seasonal Pattern," Annales d'Economie et de Statistique, ADRES, issue 61, pages 06, Janvier-M. [Downloadable!]

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