Modeling of the Deterministic Fractal Time Series by One Rule Constructors

Abstract

Tools and methods for automatic model generation for the time series’ studied class have been developed. The constructive-synthesizing model is the simplest known one thus it contains a single rule with 4-10 characters. A composite constructor, that consists of four interconnected constructors, was developed using structural synthesizing modeling tools. One of the constructors, according to the given rules, constructs a multi-symbol fractal sequence, the other transforms it into a deterministic fractal time series, the third, using the two preceding ones and genetic algorithms, finds a rule that allows the desired time series to be generated, and the fourth is a control constructor. The appropriate software has been developed. The experiments were conducted on the rules with four characters and a variable number from four to ten on the of the rule's right part. In all cases, the rules found allow accurate recreation of the original time series. The practical application of the proposed approach requires further research into stochastic time series generated by a number of rules.