Systems analysis

Metrization of the T-alphabet: measuring the distance between multidimensional real discrete sequences

A. V. Makarenko<sup>ab

a</sup> Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
^b Moscow

Abstract: The measure is proposed of discrete real sequences similarity in the extended space of states. The measure is based on the symbolic CTQ-analysis methods and is applicable to a chaotic and stochastic multidimensional non-equidistant time series as well. The analysis of the proposed metrics is carried out and their basic properties are described. The method efficiency is tested on the model systems differing in complexity and topology of the attractor. The high sensitivity of the developed similarity measures is demonstrated on the example of the financial time series analysis.

Keywords: discrete sequences, T-alphabet, metric set, symbolic analysis, financial time series, Rossler oscillator.

UDC: 519.17+519.172.4+519.246.8

 English version: Control Sciences, 2019, 80:1, 138–149