Confidence Sets for the Break Date Based on Optimal Tests

This study proposes constructing a confidence set for the date of a one-time structural change using a point optimal test. Following Elliott and Mler (2007), we first construct a test for the break date that maximizes the weighted average of the power function. The confidence set is then obtained by inverting the test statistic. We carefully choose the weights and show by Monte Carlo simulations that the confidence set based on our method has a relatively accurate coverage rate, while the length of our confidence set is significantly shorter than the lengths proposed in the literature.