The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991–2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation – the drop in the Hurst exponent – the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges – and as the developing market is less efficient – the generalization for others markets needs further investigation.