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.

中文翻译：

---

具有时空相关性的正连续数据建模

在本文中，我们专注于展示空间或时空依赖性的正数据的替代建模策略。具体来说，我们建议考虑通过 $\chi^2$ 随机过程的缩放版本的单调变换获得的随机过程。后者在专业文献中是众所周知的，起源于对平方高斯过程的独立副本求和。然而，它们作为随机模型和相关推理的使用并没有得到太多考虑。受荷兰气象站网络风速数据时空分析的启发，我们通过具有 Weibull 边际分布的非平稳过程来举例说明我们的建模策略。对于所提出的威布尔过程，我们研究了二阶和几何性质，并提供了二元分布的解析表达式。由于似然难以处理，即使对于相对较小的数据集，我们建议采用成对似然作为推理工具。此外，我们解决了预测问题，并提出了线性预测。我们的建模策略的有效性通过对上述荷兰风速数据的分析来说明，我们补充了模拟研究。