In this paper, we present the use of different mathematical models to forecast electricity price under deregulated power. A successful prediction tool of electricity price can help both power producers and consumers plan their bidding strategies. Inspired by that the support vector regression (SVR) model, with the εε-insensitive loss function, admits of the residual within the boundary values of εε-tube, we propose a hybrid model that combines both SVR and Auto-regressive integrated moving average (ARIMA) models to take advantage of the unique strength of SVR and ARIMA models in nonlinear and linear modeling, which is called SVRARIMA. A nonlinear analysis of the time-series indicates the convenience of nonlinear modeling, the SVR is applied to capture the nonlinear patterns. ARIMA models have been successfully applied in solving the residuals regression estimation problems. The experimental results demonstrate that the model proposed outperforms the existing neural-network approaches, the traditional ARIMA models and other hybrid models based on the root mean square error and mean absolute percentage error.
Accurate and efficient electricity price forecasting becomes more and more important for electricity markets. Electricity prices predictions are used for various purposes, such as speculation, derivative pricing, risk management and real option valuation. As accurate modeling of spot prices is the cornerstone of the optimal scheduling of physical assets and valuing of real options [1] and [2], intensive studies have been carried out to improve the precision.
Usually statistical based modeling techniques are used for electricity prices forecasting [3], which has advantages of simple feature and strong expansion ability, but fails to the forecasting of tremendous system’s evolution serial, especially when electricity prices system changes a lot, and classical chaos appear in the system. The traditional forecasting method too simple to simulate the complex and fast change of the electricity prices system. Chaos theory, an important discovery in nonlinear dynamic system, came into being from 1960s, until 1980s, it developed to be a new study with special concept system and method frame [4]. Artificial neural network (ANN) is an effective way to solve the complex nonlinear mapping problem, which possesses excellent robustness and error-tolerance. Among the many existing tools, the ANN has received much attention because of its clear model, easy implementation and good performance in solving nonlinear problems, and this makes it suitable for modeling and forecasting of changing complex electricity system and electricity serial. In order to increase the forecasting accuracy, it has been performed using supervised neural learning techniques [5] and [6]; while some have used an ART-type neural network [7], fuzzy clustering method and ANN [8], marquardt algorithm and feedforward networks [9], fuzzy neural network [10], wavelet transform based approach and ANN [11] and an evolutionary algorithms coupled with ANN [12].
These studies usually use BP neural network model – error reverse transform neural network, which contains a great many parameters. These parameters are always judged by experience, so the model is hard to be established [13]. Also, it has been observed that while the neural network (NN) give small error for training patterns, the error for testing patterns is usually of a larger order [14]. However support vector regression, with the εε-insensitive loss function, can overcome this shortcoming and improve the generalization capability of network. Recently, a hybrid methodology has been proposed for stock price forecasting, which applied the ARIMA model in capturing the linear patterns and the residuals are modeled by the SVR [15]. Yet the linear and nonlinear patterns could interact, and it is difficult to decide which one is the dominant part; for this reason, modeling linear patterns using linear method will change the nonlinear patterns, and vice versa. Inspired by that SVR is the preferred model for nonlinear patterns and that, compared with NN method, it keeps the linear patterns undamaged, we propose a model that combines both SVR and ARIMA models to take advantage of the unique strength of SVR and ARIMA models in nonlinear and linear modeling for short-term electricity prices forecasting, which is called SVRARIMA. The presented model is believed to greatly improve the prediction performance of the single ARIMA model and the single SVR model in forecasting electricity prices. The forecasting model adopts some tricks, such as following phase space reconstruction theory, utilizing G–P algorithm to calculate the saturation embedded dimension – the number of input level spot [16], applying ARIMA model to the residuals regression estimation problems. At last these tricks improve the generalization capability of SVR.
In this paper, the price forecasting of the California electricity market was used to examine the forecasting accuracy of the proposed hybrid model, the existing neural-network approaches, the traditional ARIMA models and other hybrid models. This study suggests that researchers and practitioners should carefully consider the nature and intended use of electricity prices data if choosing between neural networks, statistical methods and other hybrid models for electricity market management. The result of experiments proves that time serial forecasting and control system based on this method has the following advantages: (1) Better precision. (2) Smaller sampling variation effects. (3) Rather robust to parameter variation. (4) Faster response capability. (5) Compared with NN, it can keep the linear patterns undamaged relatively.
The remaining sections of this paper are organized as follows. In Section 2, the SVRARIMA model for forecasting is presented and the main steps of the method is given. Then, the possible reason behind the proposed technique is explained. In Section 3, the research design and the data description are outlined. Two performance measures are described. Obtained numerical results and comparisons are presented and discussed in Section 4. A brief review of this paper and the future research are in Section 5.
It is suspected that electricity prices time-series contain a linear and nonlinear component. Since the linear and nonlinear patterns could interact, and it is difficult to decide which one is the dominant part; consequently, modeling linear patterns using linear method will change the nonlinear patterns, and vice versa. Inspired by that SVR is the preferred model for nonlinear patterns while it keeps the linear patterns undamaged compared with NN method, we proposed a SVRARIMA approach to forecast next-week prices in the electricity market of California. The presented model is believed to greatly improve the prediction performance of the single ARIMA model and the single SVR model in forecasting electricity prices. Theoretically as well as empirically, hybridizing two dissimilar models reduces forecasting errors [33]. However, future research should address some problems. This study demonstrated that a simple combination of the two best individual models does not necessarily produce the best results. Therefore, the structured selection of the hybrid model is of great interest.
