A0452
Title: Enhancing dependence modeling with compound Archimedean and vine copulas for electricity peak demand estimation
Authors: Moshe Kelner - University of Haifa and Noga - Israel System Operator (Israel) [presenting]
Abstract: Copulas serve as an effective and elegant tool for modeling dependence between random variables. However, most copula functions possess only a single dependence parameter, thereby limiting the complexity of the dependence structure they can capture. The Archimedean family of copulas are employed, and the Archimedean inverse generator is modified to enhance the number of dependence parameters while maintaining membership in the family. This enhancement is achieved by compounding the inverse generator with a density function of the dependence parameter. The method is demonstrated using the generalized gamma distribution as a compounding density function for the inverse generator of the dependence parameter of the Clayton copula (exhibiting left tail dependence suitable for the winter peak demand) and the C2-copula (exhibiting right tail dependence suitable for the summer peak demand). This approach extends both copula functions from a single-parameter to a three-parameter function, resulting in the creation of new Archimedean families: The Clayton generalized gamma (CGG) and the Kelner-Landsman-Makov (KLM), respectively. Additionally, the conditional value at risk (VaR) is established and utilized to obtain a confidence interval for one variable given the others. A probability model is proposed for electricity peak demand using these new copula functions. Furthermore, an alternative approach using vine copulas as a means of handling dimensionality is also discussed.
