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.

翻译：我们提出了一种基于符号函数概念的自回归空间函数模型新方法，该方法将函数表示为迭代积分的无穷级数。该方法的优势在于适用于广泛的随机过程。在为所提出的模型提供理论保障之后，通过模拟研究和实际数据集验证，与传统模型相比，这种新方法展现了具有竞争力的性能表现。