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 that this new approach presents competitive performances compared to the traditional model.

翻译：我们提出了一种基于特征函数概念的空间自回归函数模型新方法。该方法通过将函数表示为其迭代积分构成的无穷级数，具有可适用于广泛过程的优势。在给出所提模型的理论保证后，我们通过仿真研究证明，与传统模型相比，该新方法展现出具有竞争力的性能表现。