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On Periodic Structures and Testing for Seasonal Unit Roots

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  • Eric Ghysels
  • Alastair Hall
  • Hahn Shik Lee

Abstract

The standard testing procedures for seasonal unit roots developed so far have been based0501nly on time invariant ARMA processes with AR polynomials involving seasonal differencing. One attractive alternative is to employ periodic ARMA models in which the coefficients are allowed to vary with the season. In this paper, we present convenient procedures for testing for the presence of unit roots at the zero and seasonal frequencies in periodic time series. The limiting distributions of these statistics are derived and tabulated. Simulation evidence illustrates the advantages of allowing for periodicity in this context when it is present. The tests are illustrated via applications to macroeconomic and ozone level data. Les procédures standards pour tester la présence de racines unitaires aux fréquences saisonnières sont basées sur une représentation invariante ARIMA. Une classe alternative de processus est celle des modèles à variations périodiques des paramètres. Dans cette étude nous présentons des tests de racines unitaires qui prennent explicitement en compte une structure périodique. Les distributions asymptotiques sont dérivées. Une étude Monte Carlo démontre les avantages de nos tests par rapport aux procédures standards.

Suggested Citation

  • Eric Ghysels & Alastair Hall & Hahn Shik Lee, 1995. "On Periodic Structures and Testing for Seasonal Unit Roots," CIRANO Working Papers 95s-21, CIRANO.
  • Handle: RePEc:cir:cirwor:95s-21
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    File URL: http://www.cirano.qc.ca/files/publications/95s-21.pdf
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    References listed on IDEAS

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    1. Ghysels, Eric & Hall, Alastair, 1990. "A Test for Structural Stability of Euler Conditions Parameters Estimated via the Generalized Method of Moments Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 355-364, May.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    4. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    5. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    6. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-1369, November.
    7. Ghysels, Eric & Hall, Alastair, 1990. "Are consumption-based intertemporal capital asset pricing models structural?," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 121-139.
    8. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 125-132.
    9. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
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    Citations

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    Cited by:

    1. Amigues, Jean-Pierre & Favard, Pascal & Gaudet, Gerard & Moreaux, Michel, 1998. "On the Optimal Order of Natural Resource Use When the Capacity of the Inexhaustible Substitute Is Limited," Journal of Economic Theory, Elsevier, vol. 80(1), pages 153-170, May.
    2. Christiano, Lawrence J. & Todd, Richard M., 2002. "The conventional treatment of seasonality in business cycle analysis: does it create distortions?," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 335-364, March.
    3. 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.
    4. Politis, Dimitris, 2016. "HEGY test under seasonal heterogeneity," University of California at San Diego, Economics Working Paper Series qt2q4054kf, Department of Economics, UC San Diego.
    5. Touhami, A. & Martens, A., 1996. "Macroemesures in Computable General Equilibrium Models: a Probabilistic Treatment with an Application to Morocco," Cahiers de recherche 9621, Universite de Montreal, Departement de sciences economiques.
    6. Kunst, Robert M., 1997. "Decision Bounds for Data-Admissible Seasonal Models," Economics Series 51, Institute for Advanced Studies.
    7. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.

    More about this item

    Keywords

    Periodic models; Seasonal unit roots; Modèles périodiques ; Racines unitaires saisonières;

    JEL classification:

    • 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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