Abstract
We propose constructing the confidence set for the emerging date of a bubble when it is detected by some tests. As the limiting distribution of the bubble date estimator changes depending on the evolving speed, it is difficult to construct the confidence interval based on the break date estimator. Instead, we consider constructing the confidence set by inverting tests for the emerging date of the bubble. The coverage rate is asymptotically controlled. The finite sample property is investigated by Monte Carlo simulations and it is found that the coverage rate in finite samples is relatively controlled well by the proposed tests without a constant, whereas the demeaned versions of the tests do not work well and the coverage rate tends to be liberal.