  Parameter estimation for and prediction of spatially or spatio--temporally
correlated random processes are used in many areas and often require the
solution of a large linear system based on the covariance matrix of the
observations. In recent years, the dataset sizes to which these methods are
applied have steadily increased such that straightforward statistical tools are
computationally too expensive to be used. In the univariate context, tapering,
i.e., creating sparse approximate linear systems, has been shown to be an
efficient tool in both the estimation and prediction settings. The asymptotic
properties are derived under an infill asymptotic setting. In this paper we use
a domain increasing framework for estimation and prediction using multivariate
tapering. Under this asymptotic regime we prove that tapering (one-tapered
form) preserves the consistency of the untapered maximum likelihood estimator
and show that tapering has asymptotically the same mean squared prediction
error as using the corresponding untapered predictor. The theoretical results
are illustrated with simulations.
