International stocks trading, currency and derivative contracts play an increasingly important role for many investors. Neural network is playing a dominant role in predicting the trends in stock markets and in currency speculation. In most economic applications, the success rate using neural networks is limited to 70 - 80%. By means of the new approach of GMDH (Group Method of Data Handling) neural network predictions can be improved further by 10 - 15%. It was observed in our study, that using GMDH for short, noisy or inaccurate data sample resulted in the best-simplified model. In the GMDH model accuracy of prediction is higher and the structure is simpler than that of the usual full physical model. As an example, prediction of the activity on the stock exchange in New York was considered. On the basis of observations in the period of Jan '95 to July '98, several variables of the stock market (S&P 500, Small Cap, Dow Jones, etc.) were predicted. A model portfolio using various stocks (Amgen, Merck, Office Depot, etc.) was built and its performance was evaluated based on neural network forecasting of the closing prices. Comparison of results was made with various neural network models such as Multilayer Perceptrons with Back Propagation, and the GMDH neural network. Variations of GMDH were studied and analysis of their performance is reported in the paper.