On Trend, Breaks and Initial Condition in Unit Root Testing

Recent approaches in unit root testing have taken into account the influences of initial condition, trend, and breaks in data using pre-testing and union of rejection testing strategies based on obtained information. This paper proposes an extension of the Harvey et al. (2012b) approach to address the case of uncertainty over the initial condition. It has been shown that this approach has low power under a large initial condition because it includes GLS-based tests. Therefore, the efficiency of some ADF-type unit root tests with breaks under various magnitudes of initial condition will be investigated, and new decision rules will be proposed. Additionally, the modification of the proposed algorithm, using pre-testing for the trend coefficient and the possible presence of multiple structural trend breaks, are also discussed. The asymptotic behaviors of all tests are analyzed under both a local-to-unity representation of the autoregressive root and a local-to-zero representation of trend and breaks magnitudes. The proposed tests show good asymptotic and finite sample properties under various magnitudes of nuisance parameters.