Signature Methods for Time Series Analysis
Main Article Content
Abstract
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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References
2. Chen K.-T. Integration of paths – a faithful representation of paths by non-commutative formal power series // Transactions of the American Mathematical Socie-ty. 1958. Vol. 89. P. 395–407. https://doi.org/10.1090/S0002-9947-1958-0106258-0
3. Lyons T. J. Differential equations driven by rough signals // Revista Ma-tematica Iberoamericana. 1998. Vol. 14. No. 2. P. 215–310. https://doi.org/10.4171/RMI/240
4. Lyons T. J., Caruana M., Levy T. Differential equations driven by rough paths // Lecture Notes in Mathematics. 2007. № 1908. https://doi.org/10.1007/978-3-540-71285-5
5. Friz P. K., Hairer M. A course on rough paths. With an introduction to regu-larity structures (2nd edition) // Springer. 2020. https://doi.org/10.1007/978-3-030-41556-3
6. Boedihardjo H., Geng X., Lyons T., Yang D. The signature of a rough path: Uniqueness. 2014. https://arxiv.org/abs/1406.7871
7. Hambly B., Lyons T. Uniqueness for the signature of a path of bounded var-iation and the reduced path group // Annals of Mathematics. 2010. Vol. 171. No. 1. P. 109–167. https://doi.org/10.4007/annals.2010.171.109
8. Graham B. Sparse arrays of signatures for online character recognition. 2013. https://arxiv.org/abs/1308.0371
9. Morrill J., Kormilitzin A., Nevado-Holgado A., Swaminathan S., Howison S., Lyons T. J. The signature-based model for early detection of sepsis from electronic health records in the intensive care unit // IEEE Conference on Computing in Cardiology. 2019. https://doi.org/10.22489/CinC.2019.014
10. Chevyrev I., Kormilitzin A. A Primer on the Signature Method in Machine Learning. 2019. https://arxiv.org/abs/1603.03788
11. Buhler H., Horvath B., Lyons T., Arribas I. P., Wood B. A data-driven market simulator for small data environments. 2020. https://arxiv.org/abs/2006.14498
12. Gyurko L. G., Lyons T., Kontkowski M., Field J. Extracting information from the signature of a financial data stream. 2014. https://arxiv.org/abs/1307.7244v2
13. Cohen S. N., Lui S., Malpass W., Mantoan G., Nesheim L., de Paula A., Reeves A., Scott C., Small E., Yang L. Nowcasting with signature methods. 2023. https://arxiv.org/abs/2305.10256v1
14. Zou H., Hastie T. Regularization and variable selection via the elastic net // Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2005. Vol. 67. No. 2. P. 301–320. https://doi.org/10.1111/j.1467-9868.2005.00503.x
15. Fermanian A. Embedding and learning with signatures // Computational Statistics & Data Analysis. 2021. Vol. 157. No. 107148. https://doi.org/10.1016/j.csda.2020.107148
16. Chevyrev I., Oberhauser H. Signature moments to characterize laws of sto-chastic processes. 2018. https://arxiv.org/abs/1810.10971
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