Energy Efficiency

, Volume 12, Issue 7, pp 1751–1769 | Cite as

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.


  1. Akpinar, M., & Yumusak, N. (2016). Year ahead demand forecast of city natural gas using seasonal time series methods. Energies, 9(9), 727. Scholar
  2. Benmouiza, K., & Cheknane, A. (2013). Forecasting hourly global solar radiation using hybrid k-means and nonlinear autoregressive neural network models. Energy Conversion and Management, 75, 561–569.CrossRefGoogle Scholar
  3. Cadenas, E., & Rivera, W. (2007). Wind speed forecasting in the south coast of Oaxaca, Mexico. Renewable Energy, 32(12), 2116–2128. Scholar
  4. Chari, A., & Christodoulou, S. (2017). Building energy performance prediction using neural networks. Energy Efficiency, 10(5), 1315–1327. Scholar
  5. DePetrillo, P. B., & Ruttimann, U. E. (1999). Determining the Hurst exponent of fractal time series and its application to electrocardiographic analysis. Computers in Biology and Medicine, 29(6), 393–406. Scholar
  6. Dong, X., Li, J., & Gao, J. (2009). Multi-fractal analysis of world crude oil prices. In Computational Sciences and Optimization, 2009. CSO 2009. International Joint Conference on (Vol. 2, pp. 489–493). IEEE.
  7. Duque-Pintor, F. J., Fernández-Gómez, M. J., Troncoso, A., & Martínez-Álvarez, F. (2016). A new methodology based on imbalanced classification for predicting outliers in electricity demand time series. Energies, 9(9), 752. Scholar
  8. Enriquez, N. (2004). A simple construction of the fractional Brownian motion. Stochastic Processes and their Applications, 109(2), 203–223. Scholar
  9. Feng, T., Fu, Z., Deng, X., & Mao, J. (2009). A brief description to different multi-fractal behaviors of daily wind speed records over China. Physics Letters A, 373(45), 4134–4141. Scholar
  10. Gao, J., Cao, Y., Tung, W. W., & Hu, J. (2007). Chaotic Time Series Analysis. In Multiscale analysis of complex time series: Integration of chaos and random fractal theory, and beyond. John Wiley & Sons.
  11. Gomes da Silva, L. M. G., & Turcotte, D. L. (1994). A comparison between Hurst and Hausdorff measures derived from fractional time series. Chaos, Solitons & Fractals, 4(12), 2181–2192. Scholar
  12. Goodwin, P., & Lawton, R. (1999). On the asymmetry of the symmetric MAPE. International Journal of Forecasting, 15(4), 405–408.CrossRefGoogle Scholar
  13. Gori, F., Ludovisi, D., & Cerritelli, P. F. (2007). Forecast of oil price and consumption in the short term under three scenarios: Parabolic, linear and chaotic behaviour. Energy, 32(7), 1291–1296.CrossRefGoogle Scholar
  14. Govindan, R. B., & Kantz, H. (2004). Long-term correlations and multifractality in surface wind speed. EPL (Europhysics Letters), 68(2), 184–190. Scholar
  15. Granderson, J., Piette, M. A., & Ghatikar, G. (2011). Building energy information systems: user case studies. Energy Efficiency, 4(1), 17–30 Scholar
  16. Hasanov, F. J., Hunt, L. C., & Mikayilov, C. I. (2016). Modeling and forecasting electricity demand in Azerbaijan using cointegration techniques. Energies, 9(12), 1045. Scholar
  17. He, Y., Xu, Q., Wan, J., & Yang, S. (2018). Electrical load forecasting based on self-adaptive chaotic neural network using Chebyshev map. Neural Computing and Applications, 29(7), 603–612. Scholar
  18. Hong, T., & Fan, S. (2016). Probabilistic electric load forecasting: A tutorial review. International Journal of Forecasting, 32(3), 914–938. Scholar
  19. Hong, T., Pinson, P., Fan, S., Zareipour, H., Troccoli, A., & Hyndman, R. J. (2016). Probabilistic energy forecasting: Global energy forecasting competition 2014 and beyond. Scholar
  20. IESO (n.d.) “IESO data directory - Ontario demand.” [Online]. Retrieved from:
  21. Jiang, P., Liu, F., & Song, Y. (2017). A hybrid forecasting model based on date-framework strategy and improved feature selection technology for short-term load forecasting. Energy, 119, 694–709. Scholar
  22. Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., & Stanley, H. E. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications, 316(1–4), 87–114. Scholar
  23. Keitsch, K. A., & Bruckner, T. (2016). Modular electrical demand forecasting framework- A novel hybrid model approach. In Systems, Signals & Devices (SSD), 2016 13th International Multi-Conference on (pp. 454–458). IEEE.
  24. Khosravi, A., Nahavandi, S., & Creighton, D. (2010). Construction of optimal prediction intervals for load forecasting problems. IEEE Transactions on Power Systems, 25(3), 1496–1503. Scholar
  25. Lee, W. J., & Hong, J. (2015). A hybrid dynamic and fuzzy time series model for mid-term power load forecasting. International Journal of Electrical Power & Energy Systems, 64, 1057–1062. Scholar
  26. Lopes, R., & Betrouni, N. (2009). Fractal and multifractal analysis: A review. Medical Image Analysis, 13(4), 634–649. Scholar
  27. Makridakis, S., Wheelwright, S., & McGee, V. (1984). Forecasting: Methods and applications (3rd ed.). New York: Wiley.Google Scholar
  28. Marinescu, A., Harris, C., Dusparic, I., Clarke, S., & Cahill, V. (2013). Residential electrical demand forecasting in very small scale: An evaluation of forecasting methods. In Software Engineering Challenges for the Smart Grid (SE4SG), 2013 2nd International Workshop on (pp. 25–32). IEEE.
  29. Marinescu, A., Dusparic, I., Harris, C., Cahill, V., & Clarke, S. (2014a). A dynamic forecasting method for small scale residential electrical demand. In Neural Networks (IJCNN), 2014 International Joint Conference on (pp. 3767–3774). IEEE.
  30. Marinescu, A., Harris, C., Dusparic, I., Cahill, V., & Clarke, S. (2014b). A hybrid approach to very small scale electrical demand forecasting. In Innovative Smart Grid Technologies Conference (ISGT), 2014 IEEE PES (pp. 1–5). IEEE.
  31. Martínez-Álvarez, F., Troncoso, A., Asencio-Cortés, G., & Riquelme, J. C. (2015). A survey on data mining techniques applied to electricity-related time series forecasting. Energies, 8(11), 13162–13193. Scholar
  32. McCauley, J. L., Gunaratne, G. H., & Bassler, K. E. (2007). Hurst exponents, Markov processes, and fractional Brownian motion. Physica A: Statistical Mechanics and its Applications, 379(1), 1–9. Scholar
  33. McGaughey, D. R., & Aitken, G. J. (2000). Statistical analysis of successive random additions for generating fractional Brownian motion. Physica A: Statistical Mechanics and its Applications, 277(1–2), 25–34. Scholar
  34. McNeil, M. A., Letschert, V. E., & Ke, J. (2013). Bottom–up energy analysis system (BUENAS) - an international appliance efficiency policy tool. Energy Efficiency, 6(2), 191–217. Scholar
  35. Moghram, I., & Rahman, S. (1989). Analysis and evaluation of five short-term load forecasting techniques. IEEE Transactions on Power Systems, 4(4), 1484–1491. Scholar
  36. Olauson, J., Bladh, J., Lönnberg, J., & Bergkvist, M. (2016). A new approach to obtain synthetic wind power forecasts for integration studies. Energies, 9(10), 800. Scholar
  37. Ortiz, J., Guarino, F., Salom, J., Corchero, C., & Cellura, M. (2014). Stochastic model for electrical loads in Mediterranean residential buildings: Validation and applications. Energy and Buildings, 80, 23–36. Scholar
  38. Paudel, S., Elmitri, M., Couturier, S., Nguyen, P. H., Kamphuis, R., Lacarrière, B., & Le Corre, O. (2017). A relevant data selection method for energy consumption prediction of low energy building based on support vector machine. Energy and Buildings, 138, 240–256. Scholar
  39. Peitgen, H. O., Jürgens, H., & Saupe, D. (2006). Chaos and fractals: New frontiers of science. Springer Science & Business Media.
  40. Piette, M. A., Kiliccote, S., & Dudley, J. H. (2013). Field demonstration of automated demand response for both winter and summer events in large buildings in the Pacific northwest. Energy Efficiency, 6(4), 671–684. Scholar
  41. Quan, H., Srinivasan, D., & Khosravi, A. (2014). Short-term load and wind power forecasting using neural network-based prediction intervals. IEEE transactions on neural networks and learning systems, 25(2), 303–315. Scholar
  42. Saupe, D. (1988). Algorithms for random fractals. In The science of fractal images (pp. 71–136). New York: Springer. Scholar
  43. Shakouri, H., & Kazemi, A. (2016). Selection of the best ARMAX model for forecasting energy demand: Case study of the residential and commercial sectors in Iran. Energy Efficiency, 9(2), 339–352. Scholar
  44. Soto, A. M., & Jentsch, M. F. (2016). Comparison of prediction models for determining energy demand in the residential sector of a country. Energy and Buildings, 128, 38–55. Scholar
  45. Tascikaraoglu, A., Boynuegri, A. R., & Uzunoglu, M. (2014). A demand side management strategy based on forecasting of residential renewable sources: A smart home system in Turkey. Energy and Buildings, 80, 309–320. Scholar
  46. Williams, K. T., & Gomez, J. D. (2016). Predicting future monthly residential energy consumption using building characteristics and climate data: A statistical learning approach. Energy and Buildings, 128, 1–11. Scholar
  47. Yuan, Y., Zhuang, X. T., & Jin, X. (2009). Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis. Physica A: Statistical Mechanics and its Applications, 388(11), 2189–2197. Scholar

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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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