Real-time monitoring of bubbles and crashes

Given the financial and economic damage that can be caused by the collapse of an asset price bubble, it is of critical importance to rapidly detect the onset of a crash once a bubble has been identified. We develop a real-time monitoring procedure for detecting a crash episode in a time series. We adopt an autoregressive framework, with bubble and crash regimes modelled by explosive and stationary dynamics, respectively. The first stage of our approach is to monitor for a bubble; conditional on which, we monitor for a crash in real time as new data emerges. Our crash detection procedure employs a statistic based on the different signs of the means of the first differences associated with explosive and stationary regimes, and critical values are obtained using a training period of data. We show that the procedure has desirable asymptotic properties in terms of its ability to rapidly detect a crash while never indicating a crash earlier than one occurs. Monte Carlo simulations further demonstrate that our procedure can offer a well-controlled false positive rate during a bubble regime. Application to the US housing market demonstrates the efficacy of our procedure in rapidly detecting the house price crash of 2006.