  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.

Methodology