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Title: A novel methodology to enriching the Archimedean family of copulas application to electricity peak demand estimation Authors:  Moshe Kelner - University of Haifa and Noga - Israel System Operator (Israel) [presenting]
Zinoviy Landsman - University of Haifa (Israel)
Udi Makov - University of Haifa (Israel)
Abstract: A copula is an effective and elegant valuable tool for modeling dependence between random variables. Among the many families of this function, one of the most prominent is the Archimedean family, which has its unique structure and features. Most copula functions in this family have only a single dependence parameter, limiting the scope of the dependence structure. A modification of the Archimedean inverse generator is presented as a way to maintain membership in the family while increasing the number of dependence parameters. This is achieved by compounding the inverse generator with a density function of the dependence parameter. The method is demonstrated using the generalized gamma as a compounding density function of the dependence parameter of the bi-variate Clayton copula inverse generator. This enriches the Clayton copula from a single parameter to a three-parameter function and generates a new Archimedean family, the Clayton generalized Gamma (CGG), that comprises several members. In addition, the conditional VaR is established and used to obtain a confidence interval of one variable given the other. Using the CGG, we propose a probability model for electricity peak demand as a function of wet. Two new measures of fit, an economic measure and a conditional coverage measure based on the conditional VaR, were introduced to select the most appropriate family member based on empirical data on daily peak demand and minimum temperature in the winter.