Spurious rejections by Dickey-Fuller tests in the presence of an endogenously determined break under the null

Leybourne et al. (1998) have proved the possibility of a `converse Perron phenomenon' when conventional Dickey-Fuller tests are applied to deter-mine the order of integration of a time series. That is, if the true generating process is I(1) but with a break, frequent spurious rejections of the null hypothesis can occur. Although Leybourne et al. (1998) suggest it would be appropriate to use procedures in which the break date was treated as endogenous, they consider it as exogenous. Thus, this paper analyses whether their results change when the structural break is identified endogenously, that is, if the break point is gleaned from the data. In this sense, applying a recursive tDF test to a unit root process which has a break in its level, there is no virtually evidence of the `converse Perron phenomenon'. For the rest of the endogeneization procedures (i.e., rolling and sequential) and for the two types of breaks considered (in level or in drift), we find, in line with Leybourne et al. (1998), some distortion in the Dickey-Fuller tDF test size, which depends on the break size, the location of the break point in the sample and the sample size.