Can one make any crash prediction in finance using the local Hurst exponent idea?

Abstract

We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is discussed. Our prediction hypothesis is verified with examples of '29 and '87 crashes, as well as with more recent phenomena in stock market from the period 1995-2003. Some interesting agreements are found.

Behavior of financial markets efficiency during the financial market crisis: 2007 – 2009

“…From the position of current research quite important are works by Grech and Mazur (2004) and Grech and Pamula (2008), who investigate a connection between the Hurst exponent and market crashes.…”

Stock Indices of BRIC economies: Explored for Non Linear Dynamics and Volatility

“…However, [7] who investigated Hurst in foreign exchange market for currencies like British Pound, Canadian Dollar, etc found that majority of foreign currencies exhibit Hurst exponent that is statistically different from 0.5 and the value changes over time. [8] used this time varying Hurst analysis to detect long term correlation in financial time series. The technique was applied in a rolling window on Dow Jones index and it was argued that Hurst may be used to detect crises.…”

Costationarity of Locally Stationary Time Series

“…Recall also the definition of rescaled time z = t/T . We conjecture that costationarity could also be made to work in the context of a whole host of other non-stationary time series models, for example, piecewise stationary GARCH models, see Andreou and Ghysels (2002) or Davis et al (2008), time-varying ARCH models, see Dahlhaus and Subba Rao (2006), Dahlhaus and Subba Rao (2007), Granger (2008), Markov-switching models, see Hamilton and Raj (2002), time-varying Hurst exponent models, see Grech and Mazur (2004) and references therein. The relations of any of these models to LSW/LSF is unclear and requires further research.…”