Note on a new Seasonal Fractionally Integrated Separable Spatial Autoregressive Model.

Summary In this paper, we introduce a new model called Fractionally Integrated Separable Spatial Autoregressive processes with Seasonality and denoted Seasonal FISSAR for two-dimensional spatial data. We focus on the class of separable spatial models whose correlation structure can be expressed as a product of correlations. This new modelling allows taking into account the seasonality patterns observed in spatial data. We investigate the properties of this new model providing stationary conditions, some explicit expressions form of the autocovariance function and the spectral density function. We establish the asymptotic behaviour of the spectral density function near the seasonal frequencies and perform some simulations to illustrate the behaviour of the model.