Space‐Time Autoregressive Hilbertian Models and Their Application for Wind Speed

We propose a novel approach for space‐time functional data analysis based on a space‐time autoregressive Hilbertian model. This model can capture the dynamic and spatial dependence of functional data over time and space. We provide sufficient conditions for the existence and uniqueness of the model and establish its asymptotic properties, such as the strong law of large numbers and the central limit theorem. We also develop a consistent estimator for the model parameters and evaluate its performance through simulations and a real example on wind speed data.