The purpose of the article is to calculate the grain production productivity indicators prediction based on the operation mechanism of a linear cellular automatic machine. The concepts of «memory depth», «long-term memory» are given, a description of the artificial intelligence method, its approbation and interpretation of the results obtained are presented. It is shown that the grain production productivity predicting develops along cyclic trajectories; their characteristics stability is significantly higher than the stability of the periodicity of separately selected process points. The article presents a demonstration of the linear cellular automaton method operation based on the time series of grain crop yields in the Ishim district of the Tyumen region.