A functional spatial autoregressive model using signatures

TL;DR

This paper introduces a novel spatial autoregressive functional model leveraging signatures, enabling flexible modeling of complex processes with theoretical guarantees and competitive empirical performance.

Contribution

It develops a new signature-based autoregressive model for spatial functional data, providing theoretical analysis and demonstrating its effectiveness through simulations and real data.

Findings

The model is theoretically sound with proven guarantees.

It performs competitively against traditional models in experiments.

Applicable to a wide range of spatial functional processes.

Abstract

We propose a new approach to the autoregressive spatial functional model, based on the notion of signature, which represents a function as an infinite series of its iterated integrals. It presents the advantage of being applicable to a wide range of processes. After having provided theoretical guarantees to the proposed model, we have shown in a simulation study and on a real data set that this new approach presents competitive performances compared to the traditional model.