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A Finite Mixture GARCH Approach with EM Algorithm for Energy Forecasting Applications

Author

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  • Yang Zhang

    (School of Economics & Finance Xi’an International Studies, University Xi’an, Xi’an 710049, China
    Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH 45221, USA)

  • Yidong Peng

    (Excelsior College, Albany, NY 12203, USA)

  • Xiuli Qu

    (Department of Industrial and Systems Engineering, North Carolina A&T State University, Greensboro, NC 27411, USA)

  • Jing Shi

    (Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH 45221, USA)

  • Ergin Erdem

    (Department of Engineering, Robert Morris University, Moon Township, PA 15108, USA)

Abstract

Enhancing forecasting performance in terms of both the expected mean value and variance has been a critical challenging issue for energy industry. In this paper, the novel methodology of finite mixture Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) approach with Expectation–Maximization (EM) algorithm is introduced. The applicability of this methodology is comprehensively evaluated for the forecasting of energy related time series including wind speed, wind power generation, and electricity price. Its forecasting performances are evaluated by various criteria, and also compared with those of the conventional AutoRegressive Moving-Average (ARMA) model and the less conventional ARMA-GARCH model. It is found that the proposed mixture GARCH model outperforms the other two models in terms of volatility modeling for all the energy related time series considered. This is proven to be statistically significant because the p-values of likelihood ratio test are less than 0.0001. On the other hand, in terms of estimations of mean wind speed, mean wind power output, and mean electricity price, no significant improvement from the proposed model is obtained. The results indicate that the proposed finite mixture GARCH model is a viable approach for mitigating the associated risk in energy related predictions thanks to the reduced errors on volatility modeling.

Suggested Citation

  • Yang Zhang & Yidong Peng & Xiuli Qu & Jing Shi & Ergin Erdem, 2021. "A Finite Mixture GARCH Approach with EM Algorithm for Energy Forecasting Applications," Energies, MDPI, vol. 14(9), pages 1-22, April.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:9:p:2352-:d:540432
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    References listed on IDEAS

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    1. Xing, Dun-Zhong & Li, Hai-Feng & Li, Jiang-Cheng & Long, Chao, 2021. "Forecasting price of financial market crash via a new nonlinear potential GARCH model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    2. Liu, Heping & Erdem, Ergin & Shi, Jing, 2011. "Comprehensive evaluation of ARMA-GARCH(-M) approaches for modeling the mean and volatility of wind speed," Applied Energy, Elsevier, vol. 88(3), pages 724-732, March.
    3. Altaf Hossain & Mohammed Nasser, 2011. "Comparison of the finite mixture of ARMA-GARCH, back propagation neural networks and support-vector machines in forecasting financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 533-551, November.
    4. Fayçal Hamdi & Saïd Souam, 2018. "Mixture periodic GARCH models: theory and applications," Empirical Economics, Springer, vol. 55(4), pages 1925-1956, December.
    5. Leisch, Friedrich, 2004. "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i08).
    6. Adedipe, Tosin & Shafiee, Mahmood & Zio, Enrico, 2020. "Bayesian Network Modelling for the Wind Energy Industry: An Overview," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    7. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    8. Emese Lazar & Carol Alexander, 2006. "Normal mixture GARCH(1,1): applications to exchange rate modelling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 307-336.
    9. Augustyniak, Maciej & Godin, Frédéric & Simard, Clarence, 2019. "A profitable modification to global quadratic hedging," Journal of Economic Dynamics and Control, Elsevier, vol. 104(C), pages 111-131.
    10. Jamil, Rehan, 2020. "Hydroelectricity consumption forecast for Pakistan using ARIMA modeling and supply-demand analysis for the year 2030," Renewable Energy, Elsevier, vol. 154(C), pages 1-10.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Wu, C.C. & Lee, Jack C., 2007. "Estimation of a utility-based asset pricing model using normal mixture GARCH(1,1)," Economic Modelling, Elsevier, vol. 24(2), pages 329-349, March.
    13. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    14. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 211-250.
    15. Erdem, Ergin & Shi, Jing, 2011. "ARMA based approaches for forecasting the tuple of wind speed and direction," Applied Energy, Elsevier, vol. 88(4), pages 1405-1414, April.
    16. Li, Gong & Shi, Jing, 2010. "On comparing three artificial neural networks for wind speed forecasting," Applied Energy, Elsevier, vol. 87(7), pages 2313-2320, July.
    17. de Oliveira, Erick Meira & Cyrino Oliveira, Fernando Luiz, 2018. "Forecasting mid-long term electric energy consumption through bagging ARIMA and exponential smoothing methods," Energy, Elsevier, vol. 144(C), pages 776-788.
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