A wavelet-based hybrid neural network for short-term electricity prices forecasting

  • Foued SaâdaouiEmail author
  • Hana Rabbouch


Forecasting is a very important and difficult task for various economic activities. Despite the great evolution of time series modeling, forecasters are still in the hunt for better strategies to improve mathematical models and come up with more accurate predictions. In this respect, several new models, mixing autoregressive processes to artificial neural networks (ANNs), have recently emerged. This is particularly the case for energy economics, where old forecasting tools are replaced by new hybrid strategies. Along the same lines, this paper aims to define a wavelet-based hybridization, involving nonlinear smooth functions, autoregressive fractionally integrated moving average (ARFIMA) model and feedforward ANNs, for electricity spot prices forecasting. The use of the wavelet decomposition in this model allows to characterize certain patterns of power time series, such as the nonlinear trend and multiple seasonal effects, and to exactly extrapolate them over the time scale. In fact, such patterns have already been pointed out as potential causes of the ANN’s inaccuracy. An ARFIMA–ANN model is then used to forecast the resulting irregular component. In the last stage, the smooth and irregular components are recombined to constitute the forecasted price. We will demonstrate the cost-effectiveness of the proposed method using hourly power prices from the Nord Pool Exchange. The testing time series consists of 52,614 observations and corresponds to the period ranging from 2012 to 2017. The results show that the new method is able to provide better interval forecasting than four benchmark models.


Forecasting Wavelets Feedforward neural networks Nonlinear fitting Hybrid models Electricity spot prices 



We would like to thank the anonymous reviewers, for their insightful and constructive comments that have greatly contributed to improving the paper, and to the editorial staff for their generous support and assistance during the review process.

Compliance with ethical standards

Conflict of interest

We declare that we are not and shall not be in any situation which could give rise to a conflict of interest in what concerns the publication of this paper.


  1. Aladag CH, Egrioglu E, Kadilar C (2012) Improvement in forecasting accuracy using the hybrid model of ARFIMA and feed forward neural network. Am J Intell Syst 2(2):12–17Google Scholar
  2. Ben Amor S, Boubaker H, Belkacem L (2018) Forecasting electricity spot price for Nord Pool market with a hybrid \(k\)-factor GARMA–LLWNN model. J Forecast 37(8):832–851MathSciNetGoogle Scholar
  3. Ben Mabrouk A, Ben Abdallah N, Dhifaoui Z (2008) Wavelet decomposition and autoregressive model for time series prediction. Appl Math Comput 199(1):334–340MathSciNetzbMATHGoogle Scholar
  4. Chaâbane N (2014) A hybrid ARFIMA and neural network model for electricity price prediction. Int J Electr Power Energy Syst 55:187–194Google Scholar
  5. Chaâbane N, Saâdaoui F, Benammou S (2012) Modelling power spot prices in deregulated European energy markets: a dual long memory approach. Glob Bus Econ Rev 14(4):338–361Google Scholar
  6. Chen K, Wang C (2007) A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan. Expert Syst Appl 32(1):254–264MathSciNetGoogle Scholar
  7. Diongue AK, Guégan D, Vignal B (2009) Forecasting electricity spot market prices with a k-factor GIGARCH process. Appl Energy 86(4):505–510Google Scholar
  8. Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62(3):531–544MathSciNetzbMATHGoogle Scholar
  9. Fard AK, Akbari-Zadeh MR (2014) A hybrid method based on wavelet, ANN and ARIMA model for short-term load forecasting. J Exp Theor Artif Intell 26(2):167–182Google Scholar
  10. Flandrin P (2004) Empirical mode decompositions as data-driven wavelet-like expansions. Int J Wavelets Multiresolut Inf Process 02(04):477–496MathSciNetzbMATHGoogle Scholar
  11. Funahashi K (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2(3):183–192Google Scholar
  12. Grané A, Veiga H (2010) Wavelet-based detection of outliers in financial time series. Comput Stat Data Anal 54(11):2580–2593MathSciNetzbMATHGoogle Scholar
  13. Granger CWJ, Joyeux R (1980) An introduction to long memory time series models and fractional differencing. J Time Ser Anal 1(1):15–39MathSciNetzbMATHGoogle Scholar
  14. Hamrita MS, Ben Abdallah N, Ben Mabrouk A (2011) A wavelet method coupled with quasi-self-similar stochastic processes for time series approximation. Int J Wavelets Multiresolut Inf Process 9(5):685–711MathSciNetzbMATHGoogle Scholar
  15. Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4(2):251–257MathSciNetGoogle Scholar
  16. Huang NE, Shen Z, Long SR, Wu MC, Shin Q, Zheng HH, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc Math Phys Eng Sci 454(1971):903–995MathSciNetzbMATHGoogle Scholar
  17. Ismail MT, Audu B, Tumala MM (2016) Comparison of forecasting performance between MODWT-GARCH(1, 1) and MODWT-EGARCH(1, 1) models: evidence from African stock markets. J Finance Data Sci 2(4):254–264Google Scholar
  18. Karthikeyan L, Nagesh Kumar D (2013) Predictability of nonstationary time series using wavelet and EMD based ARMA models. J Hydrol 502:103–119Google Scholar
  19. Lütkepohl H, Krätzig M (2004) Applied time series econometrics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  20. Mallat S (1999) A wavelet tour of signal processing. Academic Press, New YorkzbMATHGoogle Scholar
  21. Nelson M, Hill T, Remus T, O’Connor M (1999) Time series forecasting using NNs: Should the data be deseasonalized first? J Forecast 18(5):359–367Google Scholar
  22. Nowotarski J, Weron R (2018) Recent advances in electricity price forecasting: a review of probabilistic forecasting. Renew Sustain Energy Rev 81(1):1548–1568Google Scholar
  23. Pai FP, Lin CS (2005) A hybrid ARIMA and support vector machines model in stock price forecasting. Omega 33(6):497–505Google Scholar
  24. Papaioannou GP, Dikaiakos C, Evangelidis GI, Papaioannou P, Georgiadis D (2015) Co-movement analysis of Italian and Greek electricity market wholesale prices by using a wavelet approach. Energies 8(10):11770–11799Google Scholar
  25. Percival DB, Walden AT (2000) Wavelet methods for time series analysis. Cambridge University Press, CambridgezbMATHGoogle Scholar
  26. Raviv E, Bouwman KE, van Dijk D (2015) Forecasting day-ahead electricity prices: utilizing hourly prices. Energy Econ 50:227–239Google Scholar
  27. Saâdaoui F (2010) Acceleration of the EM algorithm via extrapolation methods: review, comparison and new methods. Comput Stat Data Anal 54(3):750–766MathSciNetzbMATHGoogle Scholar
  28. Saâdaoui F (2013) The price and trading volume dynamics relationship in the EEX power market: a wavelet modeling. Comput Econ 42(1):47–69Google Scholar
  29. Saâdaoui F (2017) A seasonal feedforward neural network to forecast the Nord Pool electricity prices. Neural Comput Appl 28(4):835–847Google Scholar
  30. Saâdaoui F, Mrad M (2017) Stochastic modelling of the price–volume relationship in electricity markets: evidence from the Nordic energy exchange. Int Trans Electr Energy Syst 27(9):e2362Google Scholar
  31. Saâdaoui F, Rabbouch H (2014) A wavelet-based multiscale vector-ANN model to predict comovement of econophysical systems. Expert Syst Appl 41(13):6017–6028Google Scholar
  32. Saâdaoui F, Naifar N, Aldohaiman MS (2017) Predictability and co-movement relationships between conventional and Islamic stock market indexes: a multiscale exploration using wavelets. Phys A Stat Mech Appl 482:552–568Google Scholar
  33. Sato JR, Morettin PA, Arantes PR, Amaro E Jr (2007) Wavelet based time-varying vector autoregressive modelling. Comput Stat Data Anal 51(12):5847–5866MathSciNetzbMATHGoogle Scholar
  34. Soares LJ, Medeiros MC (2008) Modeling and forecasting short-term electricity load: a comparison of methods with an application to Brazilian data. Int J Forecast 24:630–44Google Scholar
  35. Wardana ANI (2016) A comparative study of EMD, EWT and VMD for detecting the oscillation in control loop. In: International seminar on application for technology of information and communication (ISemantic), pp 58–63Google Scholar
  36. Weron R (2006) Modeling and forecasting electricity loads and prices: a statistical approach. Wiley, ChichesterGoogle Scholar
  37. Weron R (2014) Electricity price forecasting: a review of the state-of-the-art with a look into the future. Int J Forecast 30(4):1030–1081Google Scholar
  38. Yang L, Tschernig R (2002) Non- and semiparametric identification of seasonal nonlinear autoregression models. Econ Theory 18(6):1408–1448MathSciNetzbMATHGoogle Scholar
  39. Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175zbMATHGoogle Scholar
  40. Zhang GP, Qi M (2005) Neural network forecasting for seasonal and trend time series. Eur J Oper Res 160(2):501–514MathSciNetzbMATHGoogle Scholar
  41. Zhu L, Wang Y, Fan Q (2014) MODWT-ARMA model for time series prediction. Appl Math Modell 38(5–6):1859–1865MathSciNetzbMATHGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of SciencesKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Laboratoire d’Algèbre, Théorie de Nombres et Analyse Non-linéaire, Faculté des SciencesUniversity of MonastirMonastirTunisia
  3. 3.Institut Supérieur de Gestion de TunisUniversité de TunisTunisTunisia

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