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This paper shows that the spurious rejection problem illustrated by Leybourne et al. (1998) [Leybourne, S.J., Mills, T., Newbold, P., 1998. Spurious rejections by Dickey-Fuller tests in the presence of a break under the null. Journal of Econometrics 87, 191-203] is restricted to the DF type test, which is based on the conditional likelihood function discarding the first observation.
This paper examines the effects of shifts in variance on the unit root test. The limiting distribution of the test statistic is derived, and Monte Carlo experiment evidence on the finite sample is provided. This paper shows that the limiting distribution of the standard unit root test is not invariant to changes in variances. The results are supported by Monte Carlo experiments.
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