King's College London

The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), H _q, for various values of the parameter q. Using H _q, we introduce a new visual methodology to algorithmically detect critical changes in the scaling of the underlying complex time-series. The methodology involves the degree of multiscaling at a particular time instance, the multiscaling trend which is calculated by the Change-Point Analysis method, and a rigorous evaluation of the statistical significance of the results. Using this algorithm, we have identified particular patterns in the temporal co-evolution of the different H _q time-series. These GHE patterns, distinguish in a statistically robust way, not only between time periods of uniscaling and multiscaling, but also among different types of multiscaling: symmetric multiscaling (M) and asymmetric multiscaling (A). Asymmetric multiscaling can also be robustly divided into three other subcategories. We apply the visual methodology to time-series comprising of daily close prices of four stock market indices: two major ones (S&P 500 and Tokyo-NIKKEI) and two peripheral ones (Athens Stock Exchange general Index and Bombay-SENSEX). Results show that multiscaling varies greatly with time: time periods of strong multiscaling behavior and time periods of uniscaling behavior are interchanged while transitions from uniscaling to multiscaling behavior occur before critical market events, such as stock market bubbles. Moreover, particular asymmetric multiscaling patterns appear during critical stock market eras and provide useful information about market conditions. In particular, they can be used as ’fingerprints’ of a turbulent market period as well as provide warning signals for an upcoming stock market ’bubble’. The applied visual methodology also appears to distinguish between exogenous and endogenous stock market crises, based on the observed patterns before the actual events. The visual methodology is sufficiently general to be applicable for the description of the dynamical evolution of multiscaling properties of any complex system.