Statistical properties of the seasonal fractionally integrated separable spatial autoregressive model

Abstract

In this paper we introduce a new model called Fractionally Integrated Separable Spatial Autoregressive processes with Seasonality and denoted Seasonal FISSAR. 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 form of the autocovariance function and the spectral density. We also establish the asymptotic behaviour of the spectral density function near the seasonal frequencies.

Keywords: Seasonality; Spatial short memory; Seasonal long memory; Two dimensional data; Separable process; Spatial stationary process; Spatial autocovariance