In this paper, the forecasting problem of share prices at the New York Stock Exchange (NYSE) was considered and investigated. For its solution the alternative methods of computational intelligence were suggested and investigated: LSTM networks, GRU, simple recurrent neural networks (RNN) and Group Method of Data Handling (GMDH). The experimental investigations of intelligent methods for the problem of CISCO share prices were carried out and the efficiency of forecasting methods was estimated and compared. It was established that method GMDH had the best forecasting accuracy compared to other methods in the problem of share prices forecasting.