Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007–2008 credit crisis show a neat increasewith time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that themulti fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce amethod to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past.We also investigate the scaling associatedwith the tails of the logreturns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling. © 2012 Elsevier B.V. All rights reserved.