The Bottom Line

As long as investors are human, they will be subject to irrationality. Prompted by emotion, their judgments get in the way of rational behavior, making decisions that drift away from what common sense would suggest. 

The Model 

Berman Sarrazin captures irrationality in financial markets by looking for explosive movements in stock and commodity prices: when prices get out of their random walk process, they display explosive behavior, which signals a bubble in the making. 
This explosiveness is reflected by a stochastic process in which the expected value of the bubble component in the price process for the next period is greater (positive bubble) or smaller (negative bubble) than the current period’s value.
The model therefore highlights bubbles periods and gives warning signals about early formation of explosive movements.