Likelihood Ratio Tests for Seasonal Unit Roots

Abstract

This paper proposes regression‐based likelihood ratio or F tests for the seasonal unit root hypothesis which fully incorporate the implicit restrictions on the parameters associated with the deterministics. These statistics are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. The limiting representations of the statistics are presented for a general seasonal aspect. These limiting representations allow those for other scenarios concerning the deterministics to be simply obtained and provide an explanation for the similarity between critical values in apparently quite different cases of interest. We re‐examine the seasonal unit root properties of the logarithm of monthly seasonally unadjusted real industrial production in Canada.

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