Abstract <p>Signature methods are a powerful tool for use in time series analysis, transforming them into a form that is suitable for machine learning tasks. The article examines the fundamental concepts of path signatures, their properties, and their 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, and their advantages over traditional approaches are highlighted. 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.</p>