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On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation

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Author Info
Burridge, Peter
Taylor, A M Robert

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Abstract

We analyze the behavior of widely used regression-based tests for seasonal unit roots when the shocks are serially correlated. We show, in the quarterly case, that the common assumption that serial correlation may be accommodated by augmenting the test regression with appropriate lagged seasonal differences is only partially correct. The limiting null distributions of t statistics for unit roots at the zero and Nyquist frequencies are corrected by the lag augmentation, but those of t statistics at the harmonic seasonal frequency are not. Fortunately, the joint F-type tests at the harmonic frequency, which are in widespread use, do remain pivotal and should therefore supplant the individual t statistics in applied work. That the latter are indeed badly behaved in finite samples, while the F-type tests are correctly sized, is demonstrated by a Monte Carlo experiment.

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Publisher Info
Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 19 (2001)
Issue (Month): 3 (July)
Pages: 374-79
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Handle: RePEc:bes:jnlbes:v:19:y:2001:i:3:p:374-79

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  1. 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!]
  2. Peter Burridge & Frida Gjorstrup & A.M. Robert Taylor, 2004. "Robust inference on seasonal unit roots via a bootstrap applied to OECD macroeconomic series," City University Economics Discussion Papers 04/08, Department of Economics, City University, London. [Downloadable!]
  3. Robert Taylor, 2005. "On the limiting behaviour of augmented seasonal unit root tests," Economics Bulletin, Economics Bulletin, vol. 3(3), pages 1-10. [Downloadable!]
  4. Rotger, Gabriel Pons, . "Testing for Seasonal Unit Roots with Temporally Aggregated Time Series," Economics Working Papers 2003-16, School of Economics and Management, University of Aarhus. [Downloadable!]
  5. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Working Papers in Economics 170, Universitat de Barcelona. Espai de Recerca en Economia. [Downloadable!]
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  6. Robert Taylor & Peter Burridge, 2004. "Bootstrapping the HEGY Seasonal Unit Root Tests," Econometric Society 2004 North American Summer Meetings 125, Econometric Society. [Downloadable!]
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