Abstract

We propose constructing confidence sets for the emerging, collapsing, and recovery dates of a bubble by inverting tests for the location of the break date. We investigate both likelihood ratio-type tests and Elliott-Muller-type (2007) tests for detecting the break location. The limiting distributions of these tests are derived under the null hypothesis, and their asymptotic consistency under the alternative hypothesis is also established. The finite-sample properties are examined through Monte Carlo simulations. The results show that combining different types of tests is effective in controlling the coverage rate while maintaining a reasonable size of the confidence sets.