Application of vine copulas to dependence analysis of water quality data

Abstract

In this study, using vine copulas and tree sequences, dependence analysis of groundwater quality variables (Total hardness (TH), Sodium adsorption ratio (SAR), Sodium percentage (Na %) and magnesium (Mg)) was performed. For this purpose, the tree sequence of vine copulas including regular vine (R-vine), independent version of R-vine, also Gaussian version of R-vine, Gaussian independent version of R-vine, canonical vine (C-vine), independent version of C-vine, drawable vine (D-vine) and independent D-vine were evaluated independently in pairwise variables analysis. The study results of dependence structures and tree sequences of Vine copulas showed that among the studied copulas, the performance of the independent C-vine was 3.8 % better than R-vine and 0.25 % (insignificant and negligible) better than D-vine. The tree sequences provided by independent C-vine preserve correlation of pairwise variables until the last tree. In the last tree of independent C-vine, edge correlation of Mg, Na % | TH, and SAR reaches zero. Due to the proper performance of D-vine in dependence analysis of the studied variables, this copula is introduced as the selected copula.

Keywords

• 4d copula
• kendall’s tau
• tree sequence
• vine copulas