Exploring the New Age of Bubble Dates: A Fresh Look at Stock Market Behavior

You're trying to pinpoint exactly when a stock market bubble bursts or recovers. This new study builds on an earlier model by adding a fourth stage, where the market goes through a unit root process after recovering. The key here is that this model helps us accurately estimate those critical moments — the collapse and the recovery. The researchers have shown that the method works well both in the long run and in the short term. Interestingly, how fast the market recovers affects how well we can predict the end of the bubble. Another cool thing is that this model allows us to split the market data into two parts: before and after the collapse. This way, we can estimate when the market first got excited (exuberant) and when it finally calmed down (recovered) independently. This isn't just about knowing when things went wrong; it's about understanding how quickly the market bounces back.