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

2025-11-20

AI Summary

This paper addresses the uncertainty in identifying key timing events—formation, collapse, and recovery—of financial bubbles. To this end, it proposes a confidence set construction framework for structural change points based on a *test-inversion* approach. Unlike conventional single-test methods, the framework jointly incorporates likelihood-ratio–type and Elliott–Muller–type statistics, leveraging asymptotic distribution theory and Monte Carlo simulation to rigorously characterize both the asymptotic properties and finite-sample performance of change-point inference. Its key contribution lies in constructing a *joint confidence set* that aggregates multiple tests, achieving strict control of empirical coverage while substantially reducing set length—thereby enhancing both precision and robustness in timing identification. Simulation studies and empirical applications demonstrate that the method maintains reliable coverage even under multiple testing, offering a statistically sound and practically viable tool for diagnosing bubble cycles.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We propose constructing confidence sets for the emergence, collapse, and recovery dates of a bubble 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.

Problem

• Constructing confidence sets for bubble event dates
• Testing break date locations using statistical methods
• Evaluating finite-sample properties through Monte Carlo simulations

Innovation

• Constructing confidence sets by inverting break date tests
• Combining likelihood ratio and Elliott-Muller type tests
• Controlling empirical coverage with small confidence set length