On modelling positive continuous data with spatio-temporal dependence

In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of scaled version of $\chi^2$ random processes. The latter are 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 have not been much considered. Motivated by a spatio-temporal analysis of wind speed data from a network of meteorological stations in the Netherlands, we exemplify our modeling strategy by means of a non-stationary 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 relatively small data-set, we suggest to adopt the pairwise likelihood as a tool for the inference. Moreover we tackle the prediction problem and we propose a linear prediction. The effectiveness of our modeling strategy is illustrated through the analysis of the aforementioned Netherland wind speed data that we supplement with a simulation study.