Forecasting Multivariate Chaotic Processes with Precedent Analysis

Predicting the state of a dynamic system influenced by a chaotic immersion environment is an extremely difficult task, in which the direct use of statistical extrapolation computational schemes is infeasible. This paper considers a version of precedent forecasting in which we use the aftereffects of retrospective observation segments that are similar to the current situation as a forecast. Furthermore, we employ the presence of relatively stable correlations between the parameters of the immersion environment as a regularizing factor. We pay special attention to the choice of similarity measures or distances used to find analog windows in arrays of retrospective multidimensional observations.