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HEGY Tests in the Presence of Moving Averages

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  • Tomás Del Barrio Castro
  • Denise R. Osborn

Abstract

We analyze the asymptotic distributions associated with the seasonal unit root tests of the Hylleberg et al. (1990) procedure for quarterly data when the innovations follow a moving average process. Although both the t- and F-type tests suffer from scale and shift effects compared with the presumed null distributions when a fixed order of autoregressive augmentation is applied, these effects disappear when the order of augmentation is sufficiently large. However, as found by Burridge and Taylor (2001) for the autoregressive case, individual t-ratio tests at the the semi-annual frequency are not pivotal even with high orders of augmentation, although the corresponding joint F-type statistic is pivotal. Monte Carlo simulations verify the importance of the order of augmentation for finite samples generated by seasonally integrated moving average processes.
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Suggested Citation

  • Tomás Del Barrio Castro & Denise R. Osborn, 2011. "HEGY Tests in the Presence of Moving Averages," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 691-704, October.
    • Handle: RePEc:bla:obuest:v:73:y:2011:i:5:p:691-704
    DOI: j.1468-0084.2011.00633.x
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    References listed on IDEAS

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    1. del Barrio Castro, Tomas, 2006. "On the performance of the DHF tests against nonstationary alternatives," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 291-297, February.
    2. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 910-922, November.
    3. Castro, Tomas del Barrio & Osborn, Denise R., 2008. "Testing For Seasonal Unit Roots In Periodic Integrated Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1093-1129, August.
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    Cited by:

    1. Arbués, Ignacio & Ledo, Ramiro & Matilla-García, Mariano, 2016. "Automatic identification of general vector error correction models," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 10, pages 1-41.
    2. Tomás Barrio Castro & Andrii Bodnar & Andreu Sansó, 2017. "Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending," Computational Statistics, Springer, vol. 32(4), pages 1533-1568, December.
    3. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    4. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    5. 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.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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