Yuri Smetanin – Chief Researcher, Dorodnicyn Computing Centre, Russian Academy of Sciences.
Address: 40, Vavilova str., Moscow, 119333, Russian Federation.
E-mail: smetanin.iury2011@yandex.ru

Mikhail Ulyanov – Professor, Software Management Department, School of Software Engineering, National Research University Higher School of Economics.
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: muljanov@mail.ru

The main task for research of univariate and multivariate time series is improving their behavior prediction accuracy and increasing relevance of respective prediction models. In this view time series structures are studied, different classifications reflecting generating processes are introduced, and different prediction methods and mathematical tools are proposed. However time series are typically classified by one criteria which is generally quantitative instead of qualitative.

This article proposes an approach for time series study based on determination of Kolmogorov complexity of character strings which represent time series in space of words of certain alphabet. Proposed partition of values into semisegments for character coding is based on bicriteria histograming method. Obtained Kolmogorov complexity assessment data is a basis for time series complexity measure, which is one of axes in time series cluster space in character value coding. Moreover the article describes transition from character value coding to character trend coding which allows introducing additional coordinate into time series cluster space.

Further research of relationship between prediction methods and time series clusters will allow identifying the most rational methods relating to cluster groups. The most interesting and significant task is a generation of coordinate axes in cluster space in line with introduction of distance function in order to determine metric space structure in such coordinate space.