Tests of the Seasonal Unit Root Hypothesis against Heteroscedastic Seasonal Integration

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Colleges, School and Institutes


This article considers the problem of testing for a nonstochastic seasonal unit root in a seasonally observed rime 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.


Original languageEnglish
Pages (from-to)192-207
Number of pages16
JournalJournal of Business and Economic Statistics
Publication statusPublished - 1 Apr 2001


  • seasonal random walk, autoregression, randomized seasonal unit root, locally most powerful test