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Title: The seasonal fractionally integrated separable spatial autoregressive model and its properties Authors:  Papa Ousmane Cisse - Le Mans University (Senegal) [presenting]
Abdou Ka Diongue - Gaston Berger (Senegal)
Dominique Guegan - LabEx ReFi and University Paris 1 (France)
Abstract: A new model is introduced 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. The studies of spatial data have often shown presence of long-range correlation structures. To deal with this specific feature some authors had extended the long memory concept from times series to the spatial context. Thus it seems natural to incorporate seasonal patterns into the spatial model as soon as we work with data collected during many periods. This new modelling will be able to take into account periodic and cyclical behaviours presented in a lot of applications including the modelling of temperatures when the data are collected during different seasons at different locations. 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. Some methods for estimating the parameters of the Seasonal FISSAR model are also discussed.