Blockwise Euclidean likelihood for spatio-temporal covariance models

In this paper we propose a spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation we consider a general purpose graphics processing unit implementation using OpenCL. We derive the asymptotic properties of the proposed estimator and we illustrate the nite sampleproperties of our methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, we apply our estimation method to a wind component data set.