ellibsЭлектронные библиотекиRussian Digital Libraries Journal1562-5419Казанский (Приволжский) федеральный университет10.26907/1562-5419-2025-28-3-681-700ellibs-581Research ArticleСтатьиСигнатурные методы анализа временных рядовSignature Methods for Time Series AnalysisМащенкоКирилл АлексеевичMashchenkoKirill Alekseevichkirill.mashchenko@niisi.ruНИЦ «Курчатовский институт» – НИИСИNRC “Kurchatov Institute” – SRISA202523062025283681700Copyright © Мащенко К.А., 20252025Мащенко К.А.Mashchenko K.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ellibs.elpub.ru/jour/article/view/581

Сигнатурные методы представляют собой мощный инструмент анализа временных рядов, который преобразует их в форму, удобную для задач машинного обучения. В статье рассмотрены основные понятия сигнатуры пути, ее свойства и геометрический смысл, а также методы вычисления для различных типов временных рядов. Приведены примеры применения сигнатурных методов в различных областях, включая финансы, медицину и образование, продемонстрированы их преимущества перед традиционными подходами. Особое внимание уделено генерации синтетических данных на основе сигнатур, что особенно актуально в условиях ограниченного объема исходных данных. Представлены результаты экспериментальных исследований по генерации и предсказанию траекторий цифрового следа обучения студентов, подтверждающие эффективность сигнатурных методов для применения в задачах машинного обучения по анализу и прогнозированию временных рядов.

Signature methods are a powerful tool for time series analysis, transforming them into a form suitable for machine learning tasks. The article examines the fundamental concepts of path signatures, their properties, and geometric interpretation, as well as computational methods for various types of time series. Examples of signature method applications in different fields, including finance, medicine, and education, are presented, highlighting their advantages over traditional approaches. Special attention is given to synthetic data generation based on signatures, which is particularly relevant when working with limited datasets. The experimental results on generating and predicting student digital learning trajectories demonstrate the effectiveness of signature methods for machine learning applications in time series analysis and forecasting.

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The authors declare that there are no conflicts of interest present.