The impact of the initial condition on robust tests for a linear trend

This article examines the behaviour of some recently proposed 'robust' (to the order of integration of the data) tests for the presence of a deterministic linear trend in a univariate times series in situations where the magnitude of the initial condition of the series is non-negligible. We demonstrate that the asymptotic size and/or local power properties of these tests are extremely sensitive to the initial condition. Straightforward modifications to the trend tests are suggested, based on the use of trimmed data, which are shown to help reduce this sensitivity. Copyright Copyright 2010 Blackwell Publishing Ltd