Using Power Laws and the Hurst Exponent to Identify Stock Market Trading Bubbles
Rossitsa Yalamova and Bill McKelvey propose a phase-transition model of market dynamics that allows for extreme events and explains the origin of power laws in stock price volatilities as well as power laws of the autocorrelation function. Information cascading, herding, rule-based trading and so forth create a complex self-organised network among traders and leads to a power-law distribution of price volatilities. A power-law distribution punctuated with log-periodic oscillations in the index prices seems to be the signature of an impending crash. The presence of power-laws in price volatilities points to interesting dynamics. The distributions of a wide variety of events seem to follow the power-law form. The Hurst exponent was originally developed in hydrology for the practical matter of determining optimal dam-sizing for the Nile River's volatile rain and drought conditions, which had been observed over a long period of time.