Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30121
Forecasting Electricity Spot Price with Generalized Long Memory Modeling: Wavelet and Neural Network

Authors: Souhir Ben Amor, Heni Boubaker, Lotfi Belkacem


This aims of this paper is to forecast the electricity spot prices. First, we focus on modeling the conditional mean of the series so we adopt a generalized fractional -factor Gegenbauer process (k-factor GARMA). Secondly, the residual from the -factor GARMA model has used as a proxy for the conditional variance; these residuals were predicted using two different approaches. In the first approach, a local linear wavelet neural network model (LLWNN) has developed to predict the conditional variance using the Back Propagation learning algorithms. In the second approach, the Gegenbauer generalized autoregressive conditional heteroscedasticity process (G-GARCH) has adopted, and the parameters of the k-factor GARMA-G-GARCH model has estimated using the wavelet methodology based on the discrete wavelet packet transform (DWPT) approach. The empirical results have shown that the k-factor GARMA-G-GARCH model outperform the hybrid k-factor GARMA-LLWNN model, and find it is more appropriate for forecasts.

Keywords: k-factor, GARMA, LLWNN, G-GARCH, electricity price, forecasting.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 454


[1] Escribano, A., J.I. Peña, and P. Villaplana. 2011. “Modelling electricity prices: international evidence.” Oxford bulletin of economics and statistics 73: 622-650.
[2] Koopman, S.J., M. Ooms, and M.A Carnero. 2007. “Periodic seasonal Reg ARFIMA-GARCH models of daily electricity spot prices.” Journal of the American Statistical Association 102(477): 16-27.
[3] Knittel, C., and M.R. Roberts. 2005. “An empirical examination of restructured electricity prices.” Energy Economics 27(5): 791-817.
[4] Weron, R. 2006. “Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach.” The Wiley Finance Series (Book 396), Wiley, Chichester.
[5] Granger, C.W., R. Joyeux. 1981. “An introduction to long-memory time series models and fractional differencing.” Journal of time series analysis 1, 15–29.
[6] Hosking, J.R.M. 1981. “Fractional differencing.” Biometrika 68 (1): 165-176.
[7] Woodward, W.A., Q.C. Cheng, and H.L. Gray. 1998. “A k-factor GARMA long-memory model.” J Time Series Analysis 19: 485-504.
[8] Guégan, D. 2000. “A New Model: The k-factor GIGARCH Process.” Journal of Signal Processing 4: 265-271.
[9] Chen, Y., J. Dong, B. Yang, and Y. Zhang, 2004. “A local linear wavelet neural network.” Intelligent Control and Automation, IEEE: 1954-1957.
[10] Whitcher, B. 2004. “Wavelet-based estimation for seasonal long-memory processes.” Technometrics 46.
[11] Contreras, J., R. Espinola, F.J. Nogales, and A.J. Conejo. 2003. “ARIMA models to predict next day electricity prices.” IEEE Transactions on Power systems 18(3): 1014-1020.
[12] Saâdaoui, F., N. Chaâben, and S. Benammou. 2012. “Modelling power spot prices in deregulated European energy markets: a dual long memory approach.” Global Business and Economics Review 14: No. 4.
[13] Gray, H.L., N.F. Zhang, and W.A. Woodward. 1989. “On generalized fractional processes”. Journal of Time Series Analysis 10 (3): 233-257.
[14] Boubaker, H., and N. Sghaier. 2015. “Semi parametric generalized long-memory modeling of some MENA stock market returns: A wavelet approach.” Economic Modeling 50: 254-265.
[15] Caporale, G.M., L.A. Gil-Alana. 2014. “Long-run and cyclical dynamics in the US stock market.” J. Forecast. 33 (2): 147-161.
[16] Caporale, G.M., J. Cuñado, and L.A. Gil-Alana. 2012. “Modelling long-run trends and cycles in financial time series data.” J. Time Ser. Anal. 34 (2): 405-421.
[17] Ferrara, L., and D. Guegan. 2001. “Forecasting with k-factor Gegenbauer Processes: Theory and Applications.” Journal of Forecasting, Wiley 20 (8): 581-601.
[18] Diongue, A.K., D. Guégan, and B. Vignal. 2009. “Forecasting electricity spot market prices with a k-factor GIGARCH process” Applied Energy 86: 505-510.
[19] Soares, L.J., and L.R. Souza. 2006. “Forecasting electricity demand using generalized long memory.” International Journal of Forecasting 22, 17-28.
[20] Diongue, A.K., G. Dominique, and V. Bertrand. 2004. “A k-factor GIGARCH process: estimation and application on electricity market spot prices.” Probabilistic Methods Applied to Power Systems: 12-16.
[21] Beran, J. 1999. “SEMIFAR Models-a Semiparametric Framework for Modelling Trends, Long-Range Dependence and Nonstationarity”. Center of Finance and Econometrics, University of Konstanz.
[22] Baillie, R.T., T. Bollerslev, and H.O. Mikkelsen. 1996. “Fractionally integrated generalized autoregressive conditional heteroscedasticity”. J. Econ 74 (1): 3- 30.
[23] Bollerslev, T., and H.O. Mikkelsen. 19996. “Modeling and pricing long memory in stock market volatility”. J. Econometrics 73: 151-184.
[24] Boubaker, H. 2015. “Wavelet Estimation of Gegenbauer Processes: Simulation and Empirical Application”. Computational Economics 46: 551-574.
[25] Engle, R.F., 1982. “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.” Econometrica 50: 987-1008.
[26] Bollerslev, T. 1986. “Generalized autoregressive conditional heteroscedasticity”. Journal of Econometrics 31: 307-327.
[27] Boubaker; H., and M. Boutahar. 2011. “A wavelet-based approach for modelling exchange rates”. Stat Methods Appl 20: 201-220.
[28] Bordignon, S., M. Caporin, and F. Lisi. 2007. “Generalised long-memory GARCH models for intra-daily volatility”. Computational Statistics & Data Analysis 51: 5900-5912.
[29] Bordignon, S., M. Caporin, and F. Lisi. 2010. “Periodic long memory GARCH models” Econom Rev 28:60-82.
[30] Caporin, M., and F. Lisi. 2010. “Misspecification tests for periodic long memory GARCH models.” Statistical Methods & Applications 19: 47-62.
[31] Diongue, A.K., and Guégan. D. 2008. “Estimation of k-factor GIGARCH process: a Monte Carlo study.” ISSN 1955-611X.
[32] Mallat, S., and Zhang. 1993. “Matching pursuits with time-frequency dictionaries.” IEEE Transactions on Signal Processing 41: 3397-3415.
[33] Mallat, S. 1999. “A wavelet tour of signal processing”. Academic press.
[34] Pany (2011), Short-Term Load Forecasting using PSO Based Local Linear Wavelet Neural Network, International Journal of Instrumentation, Control and Automation (IJICA) ISSN : 2231-1890 Volume-1, Issue-2.
[35] Chakravarty, S., M. Nayak, and M. Bisoi. 2012. “Particle Swarm Optimization Based Local Linear Wavelet Neural Network for Forecasting Electricity Prices, Energy, Automation, and Signal (ICEAS).” Energy, Automation, and Signal (ICEAS), IEEE: 1-6.
[36] Pany, P.K., and S.P. Ghoshal. 2013. “Day-ahead Electricity Price Forecasting Using PSO-Based LLWNN Model.” International Journal of Energy Engineering (IJEE) 3: 99-106.
[37] Sharkey, A.J., 2002. Types of multinet system, in: International Workshop on Multiple Classifier Systems. Springer, pp. 108-117.
[38] Armano, G., M. Marchesi, and A. Murru. 2005. “A hybrid genetic-neural architecture for stock indexes forecasting”. Information Sciences 170: 3-33.
[39] Yu, L., S. Wang, and K.K. Lai. 2005. A novel nonlinear ensemble-forecasting model incorporating GLAR and ANN for foreign exchange rates.” Computers and Operations Research 32: 2523-2541.
[40] Taskaya. T., and M.C. Casey. 2005. “A comparative study of autoregressive neural network hybrids.” Neural Networks 18: 781-789.
[41] Tong; H., K.S. Lim. 1980. “Threshold autoregressive, limit cycles and cyclical data.” Journal of the Royal Statistical Society Series 42 (3): 245-292.
[42] Zhang, G.P. 2003. “Time series forecasting using a hybrid ARIMA and neural network model.” Neurocomputing 50: 159- 175.
[43] Khashei, M. and M. Bijari. 2010. “An artificial neural network model for time series forecasting.” Expert Syst. Appl. 37: 479-489.
[44] Valenzuela, O., I. Rojas, F. Rojas, H. Pomares, L. Herrera, A. Guillen, L. Marquez, and M. Pasadas. 2008. “Hybridization of intelligent techniques and ARIMA models for time series prediction.” Fuzzy Sets Syst. 159: 821-845.
[45] Tseng, F.M., H.C. Yu, and G.H. Tzeng. 2002. “Combining neural network model with seasonal time series ARIMA model.” Technological Forecasting & Social Change 69: 71-87.
[46] Tan. Z., J. Zhang, J. Wang, and J. Xu. 2010. “Day-ahead electricity price forecasting using wavelet transform combined with ARIMA and GARCH models.”Appl Energy 87:3606-3610.
[47] Cheung, Y.W. 1993. “Long memory in foreign-exchanges rates.” J Bus Econ Stat 11: 93-101.
[48] Ham F.H. and I. Koslanic. 2001. “Principles of Neurocompuling for Science and Engineering.” McGraw-Hill Higher Education.
[49] Khashei, M., and M. Bijari. 2011. “A novel hybridization of artificial neural networks and ARIMA models for time series forecasting.” Applied Soft Computing 11: 2664-2675.
[50] Bollerslev, T., and R. Hodrick. 1992. “Financial market efficiency tests”. The Handbook of Applied Econometrics I. Macroeconomics, North-Holland, Amsterdam.
[51] Giraitis, L., P. Kokoszka, and R. Leipus. 2000. “Stationary ARCH models: dependence structure and Central Limit Theorem.” Econometric Theory 16: 3-22.
[52] Kazakeviéius. V., and R. Leipus. 2002. “On stationarity in the ARCH(∞) model.” Econometric Theory 18: 1-16.
[53] Zaffaroni, P., 2004. “Stationarity and memory in ARCH(∞) models.” Econometric Theory 20: 147-160.
[54] Gencay, R., M.M. Dacorogna, U.A. Müller, O.V. Pictet, and R.B. Olsen. 2001. “An Introduction to High Frequency Finance.” Academic Press, London.
[55] Geweke, J., and S. Porter-Hudak. 1983. “The Estimation And Application Of Long Memory Time Series Models.” Journal of Time Series Analysis 4: 221–238.
[56] Campbell, J.Y., and S.B. Thompson. 2008. “Predicting the equity premium out of sample: can anything beat the historical average.” Rev. Finance. Stud. 21: 1509-1531.
[57] Nowotarski, J., and R. Weron. 2016. “On the importance of the long-term seasonal component in day-ahead electricity price forecasting.” Energy Economics 57: 228-235.