Bubbles and Crashes

Periodically collapsing bubbles, if they exist, induce asymmetric dynamics in asset prices. In this paper, I show that unit root quantile autoregressive models can approximate such dynamics by allowing the largest autoregressive root to take values below unity at low quantiles, which correspond to price crashes, and above unity at upper quantiles, that correspond to bubble expansions. On this basis, I employ two unit root tests based on quantile regressions to detect bubbles. Monte Carlo simulations suggest that the two tests have good size and power properties, and can outperform recursive least-squares-based tests that allow for time variation in persistence. The merits of the two tests are further illustrated in three empirical applications that examine Bitcoin, U.S. equity and U.S. housing markets. In the empirical applications, special attention is given to the issue of controlling for economic fundamentals. The estimation results indicate the presence of asymmetric dynamics that closely match those of the simulated bubble processes.