A Note on Asymmetries in Heating Degree-days and Natural Gas Consumption Dependence Structure. An Archimedean Copula Framework on the Italian System

by Alessandro Fiorini and Antonio Sileo

An important tool in order to carry out research for modeling and managing energy demand and supply is explaining variables with measures reflecting weather variations. For example, handlings with heating degree-days represent an easy way to account for almost 100% of natural gas consumption variations. Setting-up a linear model is a standard way to proceed but when the data under exam is other than linearly associated, that's to say jointly Normal distributed, correlation is no longer a measure of dependence and interpreting it as such is both theoretically and practically erroneous. In this context, statistical theory proposes a powerful tool, named copula function, to model flexible multivariate distributions in order to describe alternative dependence structures with respect to standard ones. The aim of the paper is to check whether heating degree-days are a consistent linear predictor for natural gas consumptions. In this context, a case study is developed on a monthly average of heating degree-days and monthly (residential and total) natural gas consumption volumes. Estimation results on alternative Archimedean copulas confirm that there is not sufficient evidence supporting a symmetric association with respect to the range of value variables can jointly assume. The statistical model to be used in this type of analysis should be robust against deviation from joint Normality and nesting linearity as a special case.