Application to Stock Exchange Predictions

The model of representation is adapted to predict fluctuations in stock prices. From the mathematical standpoint, neither the ‘society’, nor ‘representatives’ are necessarily human, so some objects can represent the behavior of other objects. This idea is applied to the major American and German stocks with which the Dow Jones and DAX indices are computed. For this purpose the price fluctuations of the Dow Jones stocks are regarded as representatives of those of the DAX stocks a week later. In particular, during the control period of 24 weeks, the fluctuations in

American Express

stock prices anticipated, on average, the price fluctuations of 2/3 of the DAX stocks. Some selected groups of three to five Dow Jones stocks arranged into ‘parliaments’, whose predictions are made by majority rule, have even better characteristics. Both single Dow Jones stocks and their parliaments are statistically tested on their potential to be used as predictors. For single stocks, the P-values are derived analytically; for the parliaments they are obtained by Monte Carlo simulation with 1000 experiments. The predictive capacity of the totality of Dow Jones stocks is also evaluated and statistically tested.