Nested Pattern Detection and Unidimensional Process Characterization

This document introduces methods and algorithms to characterize a series of values as patterns of repeating symbols or sequences selected with the criterion to maximize the information retrieved. The method converts a series of real-number values into texts. Then, it interprets the text from a point of view specified by several parameters. Located patterns are linked nested, with shorter sequences within longer ones. Texts are then synthesized and organized in a tree-like structure, substantially reducing entropy. The characterization of processes serves as the basis for constructing models to estimate likely projected values. Alternative ways to assess the multiscale complexity of unidimensional processes are applications of the results obtained here.