Estimation of the TQ-complexity of chaotic sequences

TL;DR

This paper introduces a new method for quantifying the complexity of multidimensional sequences, including chaotic and stochastic ones, by analyzing their trajectory shapes in extended state spaces.

Contribution

It presents a novel complexity estimation approach based on symbolic CTQ-analysis that considers sequence structure and order, applicable to various types of sequences.

Findings

Demonstrated effectiveness on financial time series

Provides a structural complexity measure for chaotic sequences

Applicable to both stochastic and deterministic sequences

Abstract

A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the structural properties of sequences and is suitable for estimating the complexity of both chaotic and stochastic sequences. It is constructed on the method, proposed earlier by the author, of symbolic CTQ-analysis of multidimensional discrete sequences and mappings. The algorithm proposed manipulates not only the frequency of occurrence of symbols, but also takes into account their sequence order. An example (financial time series) is given that demonstrates the application of the tools developed.