Generating electrical demand time series applying SRA technique to complement NAR and sARIMA models

  • Jorge L. Tena GarcíaEmail author
  • Erasmo Cadenas Calderón
  • Eduardo Rangel Heras
  • Christian Morales Ontiveros
Original Article


Prediction of demand time series is commonly approached to deliver a punctual forecast model, however, is highly recommended to provide probabilistic models that give a range to each future value of forecasting horizon. In this paper, three demand series are analyzed and forecasted by a non-linear autoregressive (NAR24) neural network and a seasonal ARIMA (sARIMA) model from which naïve prediction intervals (PI) are also computed. The error measurement for the forecast models indicated adequate accuracy and forecast performance (MAPE values under 4%), in general. As the major innovation to the literature, a methodology to provide complementary limit stochastic scenarios (LSS) for each forecast model is presented with two approaches: high consumption (HCA) and low consumption (LCA). Using fractal Brownian motion (fBm) concepts and the successive random addition technique (SRA), random walks (RW) were simulated and then added to both forecast models to generate stochastic scenarios. To start a random walk, three input parameters were determined for each case study: range, length, and Hurst coefficient (H). The most probable stochastic scenarios (PSS) accordingly to the variation coefficient were selected from all the produced scenarios. The PSS with the highest and the lowest average were selected as the limit stochastic scenarios, LSSmin and LSSmax, respectively. Total energy for the following 24 h was calculated and it showed that the range provided by LSS delivers additional information to electricity dispatchers accordingly to HCA and LCA situations which nor forecast models nor PI can foresee. Finally, in order to compare the LSS, the maximum and minimum limit scenarios were averaged to produce a stochastic “model” for each case study. Using common error measurements MAE, MSE, and MAPE, the LSS applied to NAR24 demonstrated to be more reliable in two out of three case studies.


Hurst coefficient Random walks Probabilistic forecast models High level demand Low level demand 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Facultad de Ingeniería MecánicaUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico
  2. 2.Facultad de Físico MatemáticasUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico

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