Rational spectral density models for lattice data

Conditional autoregressive CAR models, possibly with added noise, unilateral ARMA models, and directly specified correlation DC models, are widely used classes of spatial models. In this paper, we consider their generalisation to all models with a rational spectral density function. These models allow a wider range of correlation behaviour, and can provide adequate fits to data with fewer parameters. Some theoretical properties are presented, and comparisons made with CAR correlations. Some methods for estimation are discussed, and fits to some real data are compared.