  The paper is devoted to elaboration of a novel specific indicator based on
the modified Holder exponents. This indicator has been used for forecasting
critical points of financial time series and crashes of the USA stock market.
The proposed approach is based on the hypothesis, which claims that before
market critical points occur the dynamics of financial time series radically
changes, namely time series become smoother. The approach has been tested on
the stylized data and real USA stock market data. It has been shown that it is
possible to forecast such critical points of financial time series as large
upward and downward movements and trend changes. On this basis a new trading
strategy has been elaborated and tested.
