On modeling positive continuous data with spatio-temporal dependence

In this article, we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatiotemporal dependence. Specifically, we propose to consider stochastic processes obtained through a monotone transformation of scaled version of χ2 random processes. The latter is well known in the specialized literature and originates by summing independent copies of a squared Gaussian process. However, their use as stochastic models and related inference has not been much considered. Motivated by a spatiotemporal analysis of wind speed data from a network of meteorological stations in the Netherlands, we exemplify our modeling strategy by means of a nonstationary process with Weibull marginal distributions. For the proposed Weibull process we study the second-order and geometrical properties and we provide analytic expressions for the bivariate distribution. Since the likelihood is intractable, even for a relatively small data set, we suggest adopting the pairwise likelihood as a tool for inference. Moreover, we tackle the prediction problem and we propose to use a linear prediction. The effectiveness of our modeling strategy is illustrated by analyzing the aforementioned Netherland wind speed data that we integrate with a simulation study. The proposed method is implemented in the R package GeoModels.