Bat-Erdene Egshiglen: Application of signatures for forecasting

A signature is a path-transform from stochastic analysis that enjoys a certain universal approximation property. This univer- sality allows to calibrate signatures in a fast and efficient way to a wide class of problems with nonlinear dependencies. The goal of the project is to understand this approach and use it for forecasting a chosen time-series (financial data or other).

Referenciák

1. Daniel Levin, Terry Lyons, and Hao Ni. Learning from the past, predicting the statistics for the future, learning an evolving system. arXiv preprint arXiv:1309.0260, 2013.
2. Ioannis Karatzas and Steven E Shreve. Brownian motion and stochastic cal- culus. In Brownian Motion and Stochastic Calculus, pages 47–127. Springer, 1998.
3. Imanol Perez Arribas, Cristopher Salvi, and Lukasz Szpruch. Sig-sdes model for quantitative finance. arXiv preprint arXiv:2006.00218, 2020.
4. Ilya Chevyrev and Andrey Kormilitzin. A primer on the signature method in machine learning. arXiv preprint arXiv:1603.03788, 2016.
5. Lajos Gergely Gyurkó, Terry Lyons, Mark Kontkowski, and Jonathan Field. Extracting information from the signature of a financial data stream. arXiv preprint arXiv:1307.7244, 2013.

Our plan for now, in the semester, is to increase the number of paths for which we calculate the signature using or improving the old code, and after that, we plan on using actual financial data for forecasting.