Confidence Intervals for Bubble Onset and Recovery Dates
Eiji Kurozumi and Anton Skrobotov have published an article titled "Confidence Sets for the Emergence, Collapse, and Recovery Dates of a Bubble" in the journal Econometric Reviews. The paper proposes, for the first time, a method for constructing statistically justified confidence sets for the dates of financial bubble emergence, collapse, and recovery. The authors employ test inversion procedures for breakpoint location, which allows for controlled coverage rates with reasonable interval lengths. The effectiveness of the approach is demonstrated using Japanese Nikkei 225 index data.
The paper addresses the construction of confidence sets for the dates of bubble emergence, collapse, and recovery. Although methods for detecting bubbles and point estimation of their boundaries have been extensively developed in the literature, the problem of constructing confidence intervals for these dates has remained open. The authors propose an approach based on inverting tests for the location of the break date, which yields statistically justified confidence sets.
The study examines two types of tests: likelihood ratio type tests and Elliott–Müller-type tests (2007). For each of the three breakpoints — the start of the bubble, the collapse moment, and the recovery date — separate test statistics are constructed, adapted to the direction of the alternative hypothesis (leftward or rightward shift). The theoretical section derives the limiting distributions of the statistics under the null hypothesis and establishes their consistency under the alternative. Monte Carlo simulation results demonstrate that combining different types of tests (LR and EM) effectively controls the empirical coverage rate while maintaining a reasonably short length of the confidence set. The proposed methods are illustrated using the Japanese Nikkei 225 index during the Bank of Japan's monetary policy changes in 2012–2013.
Date
29 June
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