The global (based on log-periodic description) and the local (based on local fractal description) analysis of financial crash-like events is investigated and compared together on the largest developing stock market in Europe - the Warsaw stock exchange market. We show that prediction of phase transitions (crashes) based on the log-periodic approach is not exact and the final results depend strongly on the amount of data taken to make a fit. Another proposed approach is based on the investigation of temporal fluctuations in time series data signal. It is related to the local fractal dimension or to the local time dependent Hurst exponent of financial time series. We show that the latter approach works amazingly well, both for developing and developed stock markets, predicting so called rupture points in a signal in a more reliable way. The proposed method gives also information on the depth of expected correction in financial signal when the critical point has already been reached. The changes of fractal properties of financial time series after exterior interventions on the stock market are also analyzed.

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