Joint and conditional dependence modelling of peak district heating demand and outdoor temperature: a copula-based approach

  • F. Marta L. Di LascioEmail author
  • Andrea Menapace
  • Maurizio Righetti
Original Paper


This paper examines the complex dependence between peak district heating demand and outdoor temperature. Our aim is to provide the probability law of heat demand given extreme weather conditions, and derive useful implications for the management and production of thermal energy. We propose a copula-based approach and consider the case of the city of Bozen-Bolzano. The analysed data concern daily maxima heat demand observed from January 2014 to November 2017 and the corresponding outdoor temperature. We model the univariate marginal behaviour of the time series of heat demand and temperature with autoregressive integrated moving average models. Next, we investigate the dependence between the residuals’ time series through several copula models. The selected copula exhibits heavy-tailed and symmetric dependence. When taking into account the conditional behaviour of heat demand given extreme climatic events, the latter strongly affects the former, and we find a high probability of thermal energy demand reaching its peak.


Copula function Conditional probability District heating system Outdoor temperature Peak heat demand SARIMA models 



The authors are grateful to two referees for the many useful suggestions that have helped improve this paper. The first author (corresponding author F. Marta L. Di Lascio) acknowledges the support of the Free University of Bozen-Bolzano, Faculty of Economics and Management, via the project “The use of Copula for the Analysis of Complex and Extreme Energy and Climate data (CACEEC)” (Grant Nos. WW200S). The second author (Andrea Menapace) acknowledges Alperia and the Bozen-Bolzano province for providing the analysed data. The third author (Maurizio Righetti) acknowledges the support of the Free University of Bozen-Bolzano via the interdisciplinary project “Methods for optimization and integration given energy prices and renewable resources forecasts (MOIEREF)” (Grant Nos. WW2096).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019
corrected publication 2019

Authors and Affiliations

  1. 1.Faculty of Economics and ManagementFree University of Bozen-BolzanoBolzanoItaly
  2. 2.Faculty of Science and TechnologyFree University of Bozen-BolzanoBolzanoItaly

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