Confidence Sets for the Emergence, Collapse, and Recovery Dates of a Bubble

TL;DR

This paper develops methods to construct confidence sets for key dates of financial bubbles, using test inversion techniques and analyzing their statistical properties.

Contribution

It introduces a framework for separately estimating confidence intervals for bubble emergence, collapse, and recovery dates using likelihood and Elliott-Muller tests.

Findings

Combining different tests improves coverage accuracy.

Finite-sample simulations validate the proposed methods.

Asymptotic properties of tests are rigorously derived.

Abstract

We propose constructing confidence sets for the emergence, collapse, and recovery dates of a bubble separately by inverting tests for the location of the break date. We examine both likelihood ratio-type tests and the Elliott-Muller-type (2007) tests for detecting break locations. The limiting distributions of these tests are derived under the null hypothesis, and their asymptotic consistency under the alternative is established. Finite-sample properties are evaluated through Monte Carlo simulations. The results indicate that combining different types of tests effectively controls the empirical coverage rate while maintaining a reasonably small length of the confidence set.