The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market

We investigate the local fractal properties of the financial time series based on the whole history evolution (1991–2007) of the Warsaw Stock Exchange Index (WIG), connected with the largest developing financial market in Europe. Calculating the so-called local time-dependent Hurst exponent Hloc for the WIG time series we find the dependence between the behavior of the local fractal properties of the WIG time series and the crashes’ appearance on the financial market. We formulate the necessary conditions based on the Hloc behavior which have to be satisfied if the rupture or crash point is expected soon. As a result we show that the signal to sell or the signal to buy on the stock exchange market can be translated into Hloc evolution pattern. We also find a relation between the rate of the Hloc drop and the total correction the WIG index gains after the crash. The current situation on the market, particularly related to the recent Fed intervention in September ’07, is also discussed.