B0374
Title: A novel methodology to expand the Archimedean copula parameters: Application to peak demand estimation
Authors: Moshe Kelner - University of Haifa and Noga - Israel System Operator (Israel) [presenting]
Udi Makov - University of Haifa (Israel)
Zinoviy Landsman - University of Haifa (Israel)
Abstract: Relationships between variables and their accurate characterization are key to various industrial domains. In many of these relationships, a multivariate-normal distribution is often suggested, though it is inadequate since it implies that all variables follow a normal distribution. The challenge of allowing each variable to follow its own distribution can be addressed by employing copula functions, which decompose the joint probability distributions into the densities of the marginals and their dependence structures. Most of these functions have a single parameter, limiting their adaptability to data. A novel method is presented for expanding the number of parameters of Archimedean copula functions. This is accomplished by compounding the Archimedean generator with a density function of its dependence parameter. Using two different functions, one with right dependence and one with left dependence, two new rich parametric copula families are developed. This approach is applied to analyze peak electricity demand during the summer and winter seasons. These seasons are strongly influenced by maximum (right-tailed distribution) and minimum (left-tailed distribution) temperatures, respectively. The motivation is described, as the methodology used to expand copula functions, the resulting new copula families, and numerical results.
