Contemporary state of the art of financial time series modelling is connected to the Efficient Market Hypothesis according to which “prices fully reflect all available information” and hence future evolutions are unforecastable. In simple terms, EMH states that by predicting the future development we are not able to achieve the profits superior to the profits of the market index when these are adjusted for the risk and transactions costs are deducted. On the other hand, there exist works providing evidences that markets are not efficient. In these works, however, the strategies (or technical trading rules) are demonstrated to provide the extra performance in short term only and then the extra performance vanishes. In the paper we apply moving averages in order to define automated trading system and then analyze its profitability in Czech stock market. The results are statistically tested and statistical inference about the applicability of such an automated trading system in Czech stock market is made.