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Tests of the Seasonal Unit-Root Hypothesis against Heteroscedastic Seasonal Integration

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  • Taylor, A M Robert
  • Smith, Richard J

Abstract

This article considers the problem of testing for a nonstochastic seasonal unit root in a seasonally observed time series process against the alternative of a randomized seasonal root with mean unity; that is, the process displays heteroscedastic seasonal integration. The alternative hypothesis allows for potentially frequently occurring changes of regime in the process under investigation, allowing for more volatile forms of seasonal nonstationarity. We discuss a family of models that allow for a potentially smooth transition between the explosive and stationary phases of the seasonal model. To test this hypothesis we consider extensions to existing approaches developed to test against nonseasonal stochastic unit roots. Asymptotic representations of the test statistics are derived. An empirical application to a variety of quarterly measures of U.K. consumer's expenditure is also considered.

Suggested Citation

  • Taylor, A M Robert & Smith, Richard J, 2001. "Tests of the Seasonal Unit-Root Hypothesis against Heteroscedastic Seasonal Integration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 192-207, April.
    • Handle: RePEc:bes:jnlbes:v:19:y:2001:i:2:p:192-207
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    Cited by:

    1. Derek Leslie & Joanne Lindley & Leighton Thomas, 2002. "Who did worse? a comparison of US and British non-white unemployment 1970-1998," Applied Economics, Taylor & Francis Journals, vol. 34(8), pages 1041-1053.
    2. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    3. Luis Gil-Alana, 2010. "A seasonal fractional multivariate model. A testing procedure and impulse responses for the analysis of GDP and unemployment dynamics," Empirical Economics, Springer, vol. 38(2), pages 471-501, April.
    4. Karim Maher Abadir, 2004. "Cointegration Theory, Equilibrium and Disequilibrium Economics," Manchester School, University of Manchester, vol. 72(1), pages 60-71, January.
    5. Fong, Pak Wing & Li, Wai Keung, 2003. "On time series with randomized unit root and randomized seasonal unit root," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 369-395, July.

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