In this paper we propose a method called half spectral composite likelihood for the
estimation of spatial–temporal covariance functions which involves a spectral approach in
time and a covariance function in space. It facilitates the analysis of spectral density of all
possible pairwise contrasts at different spatial sites. The proposed approach requires no
matrix inversions and the estimators are shown to be consistent and asymptotically normal
under increasing domain asymptotic in a fashion similar to Bevilacqua et al.(2012). A …