A multivariate spatial regression model using signatures

TL;DR

This paper introduces a multivariate spatial regression model utilizing signatures to effectively handle functional covariates, with theoretical guarantees and demonstrated superior performance in pollution data analysis.

Contribution

The paper presents a novel spatial autoregressive model based on signatures, providing theoretical insights and empirical evidence of improved accuracy over existing methods.

Findings

Outperforms existing approaches in pollution data analysis

Provides theoretical guarantees for signature truncation

Applicable to a wide range of processes

Abstract

We propose a spatial autoregressive model for a multivariate response variable and functional covariates. The approach is based on the notion of signature, which represents a function as an infinite series of its iterated integrals and presents the advantage of being applicable to a wide range of processes. We have provided theoretical guarantees for the choice of the signature truncation order, and we have shown in a simulation study and an application to pollution data that this approach outperforms existing approaches in the literature.