Global and local regression: a signature approach with applications
Abstract
The path signature is a powerful tool for solving regression problems on path space, i.e., for computing conditional expectations E[Y | X] when the random variable X is a stochastic process -- or a time-series. We provide new theoretical convergence guarantees for two different, complementary approaches to regression using signature methods. In the context of global regression, we show that linear functionals of the robust signature are universal in the Lp sense in a wide class of examples. In addition, we present a local regression method based on signature semi-metrics, and show universality as well as rates of convergence. Based on joint works with Davit Gogolashvili, Luca Pelizzari, and John Schoenmakers.
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Christian Bayer obtained his PhD at the TU Vienna on numerical methods for stochastic differential equations. He is working as a Senior Researcher at the Weierstrass Institute of Applied Analysis and Stochastics in Berlin. His research interests are in rough volatility, computational finance, stochastic numerics, and stochastic optimal control.