In this paper we provide a joint treatment of two major problems that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, and uncertainty as to whether the initial condition of the process is (asymptotically)...

Recently, Mukherjee and Bandyopadhyay (J Stat Plan Inference, <CitationRef CitationID="CR28">2011</CitationRef>, doi:<ExternalRef> <RefSource>10.1016/j.jspi.2011.02.017</RefSource> <RefTarget Address="10.1016/j.jspi.2011.02.017" TargetType="DOI"/> </ExternalRef>) introduced some partially sequential tests for detecting liner trend among the incoming series of observations when a training sample is available a-priori. Their work is very useful in...</refsource></externalref></citationref>

We compare the asymptotic local power of upper-tail unit root tests against an explosive alternative based on ordinary least squares (OLS) and quasi-differenced (QD) demeaning/detrending. We find that under an asymptotically negligible initialisation, the QD-based tests are near asymptotically...