Joint and conditional dependence modelling of district heating demand and weather conditions: a copula-based approach
Di Lascio FML
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We analyze the dependence relationship between district heating demand and weather conditions, such as outdoor temperature and solar radiation, through copula function. Copula function makes it possible to represent complex associations among variables for many different dependence structures of the data generating process without requiring specific distributional forms for the margins. Thus, copula is a flexible tool to model complex and multivariate relationships. Our aim is to derive the conditional copula of heat demand given weather conditions, with particular attention to extreme climatic events, in order to provide useful implications for the management and production of thermal energy. We consider the case of the city of Bozen-Bolzano (Italy) and data concern district heating demand observed from January 2014 to November 2017. The methodology used comprises three steps. First, the univariate marginal probability distribution of the variables of interest are estimated though a seasonal autoregressive moving average model for time series using the well-known Box&Jenkins procedure. Thus, we account for the non-stationarity of each time series, and model the serial dependence structure in the time series taken separately. Next, the residuals of the estimated models are computed and, being non-autocorrelated, they enable resorting to copula theory. In the second step of the analysis, we, Indeed, model the complex cross-dependence relationship between heat demand and weather conditions through several different models. The most appropriate copula is selected on the basis of the empirical quantile dependence plot, the Akaike information criterion and the goodness-of-fit copula test. Finally, we derive the conditional probability function of heat demand given weather conditions. The analysis of the percentiles of such conditional distribution shows that the proposed approach can be a potentially powerful tool to improve the management of thermal energy and its storage in district heating systems.
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