A robust least square approach for forecasting models: an application to Brazil’s natural gas demand

  • Oswaldo L. V. CostaEmail author
  • Celma de Oliveira Ribeiro
  • Linda Lee Ho
  • Erik Eduardo Rego
  • Virginia Parente
  • Javier Toro
Original Paper


The robust least square method has been introduced in the literature as a new parameter estimation technique to deal with the presence of data uncertainties. In this paper we propose to use the robust least square method combined with log-linear Cobb–Douglas model as an alternative for developing forecast models. We first extend the robust least square method to the case which allows uncertainties only in some columns of the data matrix as well as to include weighting matrices on the past data observations and on the uncertainties. Afterwards we compare the robust and ordinary least square methods for the yearly estimate for the natural gas demand in Brazil, considering the total demand as well as the industrial and power sectors demand. Regarding the power sector case, a further contribution of the paper is to analyze the impact of the reservoirs’ levels over the demand of natural gas by thermoelectric power plants in an energy mix dominated by hydropower. Although both methods, the robust and the ordinary least square, presented similar results, the robust approach gave a slightly better result and presented reasonable long-run elasticities related to the demand of natural in the country, indicating that can it be a good alternative to overcome the difficulties associated with the use of short time series and unreliable data on the forecast of energy consumption in emerging markets.


Robust least square Second order cone programming Demand forecast Natural gas in Brazil 



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Copyright information

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

Authors and Affiliations

  1. 1.Department of Telecommunications and Control EngineeringEPUSP-Polytechnic School of the University of São PauloSão PauloBrazil
  2. 2.Department of Production EngineeringEPUSPSão PauloBrazil
  3. 3.Graduate Energy Program of the Institute of Energy and Environment at the University of São PauloSão PauloBrazil

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