Rosa M. Espejo, Nikolai N. Leonenko, María D. Ruiz-Medina
January 16, 2014

### Abstract

Abstract. This paper introduces spatial long-range dependence time series models, based on the consideration of fractional difference operators associated with Gegenbauer polynomials. Their structural properties are analyzed. The spatial autoregressive Gegenbauer case is also studied, including the case of k factors with multiple singularities. An extension to the Hilbert-valued context is finally formulated leading to the introduction of a new class of spatial functional time series models.