The pair-copula construction in space and time: a new approach to model spatio-temporal dependencies

Copula是一个统计概念，能够对随机变量之间的任何依赖关系进行建模。捕捉极端数据的非高斯依赖性使其在金融风险评估中很受欢迎。非高斯依赖性也可以在许多时空数据集中找到。与经典方法相比，非高斯，特别是不对称的依赖关系可以很容易地捕获与copula。利用copula函数改进了偏斜数据的插值。此外，Copula使我们能够评估极端事件的风险。Copula是时空地质统计学中的一个新概念。挑战在于找到适合数据集的合适copula。与多元copula相反，二元copula已经被很好地理解，并且自然不那么复杂。一个非常有前途的算法，利用简单的二元copula和建设多元的是对copula建设（PCC）已成功地应用于金融多元时间序列。在时空背景下，一对copula的维数取决于所涉及的点的数量。同样地，构建成对copula的二元copula的数量将以二次方增长。为了克服这个问题，我们将开发快速估计程序和智能算法，减少对copula的数量进行估计。此外，我们将以自给自足的方式实施这些程序，以实现自动化处理。PCC将与其他最近的方法进行比较，并应用于两个用例。

Copulas are a statistical concept capable of modelling any kind of dependence between random variables detached from their margins. Capturing the non-Gaussian dependencies of extreme data made them popular in financial risk assessment. Non-Gaussian dependencies can also be found in many spatio-temporal datasets. In contrast to classical approaches, non-Gaussian and in particular asymmetric dependencies can easily be captured with copulas. Exploiting copulas improves the interpolation of skewed data. Furthermore, copulas enable us to assess the risk of extreme events. The concept of copulas is new to the domain of spatio-temporal Geostatistics. The challenge is to find a suitable copula that fits the dataset. In contrast to multivariate copulas, bivariate copulas are quite well understood and are naturally less complex. A very promising algorithm exploiting the simplicity of bivariate copulas and constructing multivariate ones is the pair-copula construction (PCC) which has been successfully applied to multivariate time series in finance. In the spatio-temporal context, a pair-copula’s dimension depends on the quantity of points involved. Likewise, the number of bivariate copulas building up the pair-copula will grow quadratic. To overcome this issue we will develop fast estimation procedures and smart algorithms reducing the number of pair-copulas to be estimated. Furthermore, we will implement the procedures in a self-sufficient manner to allow for an automated processing. The PCC will be compared with other recent approaches and applied to two use-cases.