Quantile analysis for financial bubble detection and surveillance

Understanding and monitoring financial bubbles is critical, as they can lead to market instability, asset price crashes, and economic downturns with widespread consequences. This article explores the usefulness of quantile regression (QR) technique in detecting and surveilling financial bubbles, encompassing both global testing and real-time monitoring. We demonstrate that the QR-based quantile unit root test, coupled with an optimal quantile selection technique, serves as an effective tool for a global bubble test without necessitating additional recursive techniques. Moreover, we propose two QR-based bubble monitoring techniques. We show that the monitoring statistics follow a random variate under the null hypothesis of no bubbles but diverge to positive infinity in the presence of a mildly explosive bubble, and hence consistently date the origination of a bubble. Monte Carlo simulations suggest that compared with their LS counterparts, in the presence of skewed distributions, the QR-based global test delivers substantially greater power, while the QR-based monitoring procedures offer higher bubble detection rate and more accurate dating of the bubble origination. As an illustration, we conduct a pseudo real-time monitoring exercise with the S&P 500 composite index.