We define a method for predicting the stochastic behavior of the Bull and Bear periods of the stock market. In this paper, initially, we carry on a comprehensive evaluation of more frequently used statistical methods for evaluating Stock markets. Our work is based on collecting 40 years of data from the Italian stock market. The proposed solution is defined using the statistical analysis of the Bear and Bull Stock markets. We defined a new system to predict the trend of a stock market price, where the trend of the succession of Bull and Bear markets can be described by a probability density function given by a Gaussian distribution. Furthermore, we consider the inverses of the relative time intervals as a measure of the speed with which the phenomenon of the Bear market (or, equivalently, the Bull market) develops in that interval of time. Therefore, this factor can ultimately represent the first statistical weight of the single percentage variation. Again, the time intervals of the individual Bear and Bull market periods are considered, calculated from 01/01/1973. This allows us to consider the hypothesis that a secondary factor of probability is the temporal distance of the event that has already occurred. This work includes a criterion for statistically generating the most probable values of the next Bear and Bull markets and the length of the time intervals corresponding to these market situations. This criterion is based on the following hypothesis:
To obtain the distribution of the predictive points of max and min in the succession of Bull and Bear markets, it is assumed that, in the long period, the random distribution of the successive max and min takes the trend of the distribution of the distance fluctuations between the zeroes of the Riemann's function which, in turn, is approximated by a Unitary Gaussian Distribution (GUE). Our results show that:
- The linear interpolation of the Variations of the market (positive and negative) relative to different and successive sampling sets for future trends do not show high percentage variations between them,
- Above all, the lengths of the single time intervals of the future variations, relative to different and successive sampling sets, are quite similar to each other. Hence, the method appears to be basically stable and promising.