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.
Highlights
The main contributions of this research lie in two aspects: (1) the innovative approach of combining finite mixture Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) and EM algorithm is for the first time proposed such that non-normal distributions could be handled and the parameter estimation could be processed efficiently; and (2) the proposed method is found to be superior in terms of volatility modeling compared with the traditional GARCH models based on the comprehensive evaluation of three types of energy time series data
The results indicate that the finite mixture ARMAGARCH model outperforms the other two methods in terms of directional symmetry (DS) and weighted directional symmetry (WDS)
Given the error term ε t from AutoRegressive Moving-Average (ARMA)(p, q) model, the finite mixture GARCH model assumes that ε t follows a Gaussian mixture distribution, i.e., 2, · · · σ2 ), where w is the weight for the kth Gaussian ε t ∼ N M
Summary
Volatility prediction is a major consideration for energy-related processes or variables, which include, but are not limited to, oil prices, energy consumptions, electricity prices, energy generations from traditional and renewable sources, and meteorological variables such as wind speed. We develop the finite mixture GARCH models with the help of EM algorithm and compare their prediction performances with those of the traditional ARMA and ARMA-GARCH models. The main contributions of this research lie in two aspects: (1) the innovative approach of combining finite mixture GARCH and EM algorithm is for the first time proposed such that non-normal distributions could be handled and the parameter estimation could be processed efficiently; and (2) the proposed method is found to be superior in terms of volatility modeling compared with the traditional GARCH models based on the comprehensive evaluation of three types of energy time series data.
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