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We propose a functional linear autoregressive spatial model where the explanatory variable takes values in a function space while the response process is real-valued and spatially autocorrelated.
The specificity of the model is the functional nature  of the explanatory variable and the structure of a spatial weight matrix which defines the spatial relation and dependency between neighbors. The  estimation procedure consists in reducing the infinite dimension of the functional explanatory variable and maximizing a quasi-maximum likelihood. We establish both consistency and asymptotic normality of the regression parameter function estimate. We illustrate the skills of the methods by some numerical results