Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach

Abstract

In the last years there has been a growing interest in the construction space-time covariance functions. However, effective estimation methods for these models are some- how unexplored. In this paper we propose a composite likelihood approach and a weighted variant for the space-time estimation problem. The proposed method can be a valid compromise between the computational bur- dens, induced by the use of a maximum likelihood approach, and the loss of efficiency induced by using a weighted least squares procedure. An identification criterion based on the composite likelihood is also introduced. The effectiveness of the proposed pro- cedure is illustrated through an extensive simulation experiment, and by reanalising a data set on Irish wind speeds (Haslett and Raftery, 1989). We also address an im- portant issue, which has been recently explored in the literature, on how to select an appropriate space-time model by accounting for the tradeoff between goodness-of-fit and model complexity.