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Identification of periodic patterns in time series

Keywords:

T.V. Afanasjeva – Dr. Sc. (Eng.), Professor, Associate Professor, Department «Information Systems»,
Ulyanovsk State Technical University
E-mail: tv.afanasjeva@gmail.com
A.A. Sapunkov – Post-graduate Student, Ulyanovsk State Technical University
E-mail: sapalks@gmail.com
V.M. Stuchebnikov – Dr. Sc. (Eng.), Professor, General Director, JSC MIDAUS (Ulyanovsk)
E-mail: mida@mv.ru


Preprocessing and time series analysis is an important task in the field of process analysis. One of the tasks of the analysis is the task of detecting of events and their periods to simulate periodic and seasonal changes in time series. Known solutions rely on algorithms that are partly based on knowledge of the possible behavior of a time series or its model, which requires the involvement of an expert. However, when working with large volumes of data, the work of experts becomes less effective.
The article proposes the solution of the problem of identification of periodic patterns and their characteristics in linguistic time series. It is assumed that the numerical time series has been previously converted into linguistic one. Symbolic and segmental periodicity, represented in the form of linguistic patterns, repeated at regular intervals of time, are considered. The article introduces the definitions and statements that differentiate the notion of periodicity into symbolic and segmental. An algorithm for detecting periodicity in time series is proposed, which makes it possible to identify the parameters of repeating patterns with a constant period.
The proposed algorithm consists of two stages: the search for all repeating patterns in the linguistic time series and testing the pa-rameters of the generated patterns for the periodicity. The use of linguistic time series allows you to use a modified suffix tree (a pattern tree) to search for repeated patterns. Modifications of the algorithm for constructing this tree are aimed at obtaining the parameters of the patterns. At the second stage of the algorithm, each pattern is tested for repeatability with a constant period. The result of the proposed algorithm is the conclusion about the presence or absence of periodicity in the time series, as well as the parameters of the periodic patterns, which makes it possible to apply this information to their prediction.

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