Unobserved heterogeneity in Markovian analysis of the size distortion of unit root tests

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Abstract
We confirm that units root tests can exhibit substantial size distortion when breaks in mean are generated by a first-order Markov chain, but unlike previous literature, we find augmentation largely remedies this situation. However, considerable heterogeneity is evident in the size properties of the tests when faced with breaks in mean varying in duration, in number and in position within the sample. This heterogeneity will be hidden when a Markov chain is employed. For instance, when the transition probabilities generate single period outliers, rejection frequencies (RFs) rise substantially with the number of outliers, but augmentation results in approximately nominal RFs. Qualitatively similar results hold when a number of structural breaks are allocated randomly in the central section of the sample. Interestingly, very different behaviour is exposed by a design exploring the impact on the tests of two breaks imposed at a range of fixed intervals, RFs rising when break occur in the extremities of the sample, a situation unaffected by augmentation.

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