Some contributions on the characterization of one-dimensional spatial processes

The characterization of one-dimensional spatial processes is considered. Specifically, expressions for rational, continuous, two-sided impulse response (IR) functions corresponding to different rational factorizations of the spectral density function of continuous ARMA(p,q) models are derived. Furthermore, with the restriction on the continuity of IR at the origin, certain models are found to be inadmissible representation of space series. The possible applications of the results deduced in this paper are also presented.