The discontinuous trend unit root test when the break point is misspecified

Dickey and Fuller proposed some tests for the unit root hypothesis in uni-variate time series. [P. Perron, The great crash, the oil price shock, and the unit root hypothesis, Econometrica 57 (1989) 1361–1401] extended the t-ratio type unit root tests so that they allow for a break in the deterministic trend and/or in the intercept term. The purpose of the paper is to study by simulations the effect of a misspecified break point on the tests proposed by Perron. Further, the limits of the test statistics by Perron are derived under the assumption of a misspecified break point, and the accuracy of the limit formula is examined by simulation techniques. Finally, a test is proposed which jumps the break interval instead of a break point.