Estimating space-time covariance functions: a composite likelihood approach

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 somehow 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 burdens, 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 procedure 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 important 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.