The implementation of modern neural network technology in the financial indexes modelling and forecasting task is given in this paper. The predicted value is Dow Jones Riga Stock Exchange index, which characterises Latvian stock market. Using Dow Jones RSE index time series a number of neural network learning experiments are completed, the best network is selected and the index values are predicted for month ahead. The same prediction is made using Box-Jenkins model. The results of both of methods are compared and conclusions are presented.