Half spectral composite likelihood approach for estimating spatial–temporal covariance functions

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 simulation study is carried out to assess the performance of the proposed estimation method from statistical and computational viewpoint with respect to difference composite likelihood. The half spectral composite likelihood estimates show better performance with respect to the difference composite likelihood. A real example is given using the Irish wind speed data.