Deciding Break Interval in the Discoutinuous Trend Unit Root Test

Dickey and Fuller proposed the tests for unit root hypotheses in a uni-variate time series. Perron[1989] extended the t-ratio type unit-root tests so that they allow for a break in the deterministic trend and/ orin the intercept term. In practice, it seems difficult to specify the break point correctly. Zivot and Andrews[1992] proposed a test in which the break point is statistically determined. Morimune and Nakagawa [1999]studied the effect of a miss specified break point on the Perron tests, and the accuracy of the asymptoticexpression is examined under various specifications of the error. This paper proposes to set an interval thatpossibly covers a break point in the Perron tests. This helps to avoid miss specifying the break point, and theunit root test is less susceptible to the choice of a particular break point. Furthermore, an orthogonaldecomposition of the F-ratio type test is proposed to find the correlation between the first difference of theseries and the trend.