Oxford Bulletin of Economics and Statistics

Trend and Initial Condition in Stationarity Tests: The Asymptotic Analysis

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Abstract

In this article, we investigate the behaviour of stationarity tests proposed by Müller [Journal of Econometrics (2005) Vol. 128, pp. 195–213] and Harris et al. [Econometric Theory (2007) Vol. 23, pp. 355–363] with uncertainty over the trend and/or initial condition. As different tests are efficient for different magnitudes of local trend and initial condition, following Harvey et al. [Journal of Econometrics (2012) Vol. 169, pp. 188–195], we propose decision rule based on the rejection of null hypothesis for multiple tests. Additionally, we propose a modification of this decision rule, relying on additional information about the magnitudes of the local trend and/or the initial condition that is obtained through pre‐testing. The resulting modification has satisfactory size properties under both uncertainty types.

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