Signature-based Methodology for Time Series Statistical Analysis

XIN GUO – UNIVERSITY OF CALIFORNIA, BERKELEY

ABSTRACT

Signature transform has recently gained significant attention in the theory of stochastic analysis. In this talk, I will discuss how the signature transform can be exploited to address several long standing challenges in analyzing time series data, which  are typically non-stationary, nonlinear, and often fragmented, and for which modern deep learning models are inappropriate due to limited interpretability and in principle require large volumes of training data.  In particular, we propose a simple signature-based adaptive Lasso approach that has been successfully developed and implemented in industry. This method addresses many of the challenges mentioned above while demonstrating strong potential for a wide range of applications.

The talk will begin with a brief introduction to the signature transform, which has its origins in topology and has been extensively developed within the rough path theory. We will then review the key properties of the signature transform that are most relevant to our statistical methodology. The talk is intended to be self-contained.