Forecast a one-dimensional stochastic automaton

In this work we show an alternative form for forecasting trends in time series that behaves stochastically. For this, we are adopting a mathematical approach and treating the time series as the evolution of stochastic cellular automata, and thus, our problem narrows down to find the model for the cellular automata that best describes the behavior of time series. Using machine learning, more specifically genetic algorithm, we indicate the methodology for adjusting the vector of probabilities that define the model of Stochastic Cellular Automata (SCA). Previous results have shown that the methodology presented guarantee 100% of hit for deterministic models, according to tests applied to 256 models of deterministic automata presented by Stephen Wolfram. As far as the results based on stochastic models are concerned, initial studies confirm the validity of the methodology and assign an alternative mathematical method to the problem of stochastic forecasting.