Forecasting wavelet neural hybrid network with financial ensemble empirical mode decomposition and MCID evaluation
Introduction
Energy is an indispensable material basis for sustainable economic and social development. With the development of economic globalization and financial liberalization, the energy futures market has been developing rapidly, showing an increasingly important trend in the energy market. The erratic fluctuations of energy market prices have increased the investment risks of investors and brought influence to the development of economic and social (He et al., 2010, Huang et al., 2020, Kang et al., 2015). In addition, energy market prices are closely related to other markets, such as the stock market. For example, some scholars have analyzed the relationship between energy prices and stock prices in some countries (Cunado and de Gracia, 2014, Delgado et al., 2018, Fang and You, 2014, Sun et al., 2019, Wen et al., 2012). Thus, the forecast analysis of energy market prices is particularly important. Due to the complex nature of energy prices, forecasting becomes more difficult. Efforts to improve forecasting accuracy have been the focus of research by many scholars in recent years (Cen and Wang, 2019, Wang and Wang, 2016).
In terms of time series forecasting, artificial neural network has made great progress, which is a mathematical method of simulating human actual neural networks (Xu et al., 2019, Yao, 1999, Zhang et al., 1998). Generally, the neural network construction model is divided into the following two cases: forward modeling and reverse modeling. So far, the number of neural network models has been about forty, such as back-propagation neural networks, convolutional neural networks (Goh, 1995, Kristjanpoller et al., 2014, Lin et al., 2009, Ting et al., 2019). Artificial neural network has been applied to various fields in time series prediction. Adamowski and Chan (2011) put forward a new method based on coupling discrete wavelet transforms and artificial neural networks for groundwater level forecasting applications. Kristjanpoller and Minutolo (2015) applied the artificial neural network to the generalized autoregressive conditional heteroskedasticity method to generate a hybrid model to forecast the gold price volatility. Besides, they extended previous research to the area of oil price volatility and the hybrid model increased the volatility forecasting precision (Kristjanpoller & Minutolo, 2016). Mo et al. (2016) proposed the exponent back propagation neural network to predict the cross-correlations between two financial time series. A novel clustering-enhanced adaptive artificial neural network model was used to forecast 24h-ahead building cooling demand in subtropical areas (Luo, 2020). Due to its strong generalization and learning ability as well as adaptability, in this paper, we use the artificial neural network to improve the forecasting accuracy of energy prices.
Wavelet neural network (WNN) is an artificial neural network established in recent years which is based on wavelet transform (Zhang and Benveniste, 1992, Zhang and Kon, 2017). The wavelet transform uses dilation and translation for multi-scale analysis of signals, furthermore it can efficaciously from time domain and frequency domain of stationary or non-stationary signals to extract information (Ford, 2003, Minutolo et al., 2018, Stocchi and Marchesi, 2018). Compared with the forward neural network, WNN has obvious advantages. First of all, the basic element and overall structure of WNN model can avoid blindness compared with the back-propagation neural network and other structures. What is more, WNN has stronger learning ability and higher precision. Generally, for a learning task, WNN structure is simpler, the speed of convergence is quicker, and the precision is greater (Zhang et al., 1995). Wavelet neural network was found to be more effective and robust than multilayer perceptron, which was employed to predict three gasoline properties in 2008 (Balabin et al., 2008). Zhang and Yu (2010) has proposed a prediction model of gold price based on wavelet neural network, which has the higher precision and speed than back-propagation neural network. In recent years, in order to improve the prediction accuracy, more and more researchers combine decomposition method with neural network to build a hybrid model to predict time series (Tan et al., 2018). For instance, an empirical mode decomposition based neural network ensemble learning paradigm was proposed for world crude oil spot price forecasting (Yu et al., 2008). Huang and Wang (2018) combined the discrete wavelet transform and stochastic recurrent wavelet neural network to structure a novel hybrid model to improve the prediction accuracy of energy prices. Wu et al. (2018) proposed a novel model based on ensemble empirical mode decomposition and long short-term memory for forecasting crude oil price.
In fact, there are many factors interacting in the energy futures price series. The traditional prediction model only conducts forecasting based on historical data without considering the behavior of the market, resulting in poor accuracy. Since the early historical data represents the market information at that time, it will also have an impact on the current forecast results. Therefore, both early data and recent data should be considered. But the degree of data impact at different times is also different. In general, closer to the present time of the historical data in the market, the influence is greater. Thus, we use stochastic process theory to express the extent to which historical data influences the market (Niu and Wang, 2013, Yu and Wang, 2012). In the operation of random time-dependent neural network algorithm, each set of historical data will be given different weights due to its appearance time and importance to the late prediction. In addition, be grounded on principle of noise-assisted signal processing, the ensemble empirical mode decomposition method decomposes the original time series into different components with high and low frequency. By considering the properties of nonlinear data and the impact of historical data, this paper puts forward a hybrid forecasting model which is used to predict energy price series called the EEMD-WNNRT forecasting model to improve the prediction accuracy of energy prices. It integrates ensemble empirical mode decomposition (EEMD) into the wavelet neural network with random time effective (WNNRT) model. It provides a more accurate forecasting method for energy prices prediction.
The rest of the paper is listed as follows. Section 2 presents the algorithm of proposed predictive model. Section 3 introduces the selected data, which are West Texas Intermediate Crude Oil (WTI), Brent Crude Oil (BRE), Occidental Petroleum Corporation (OXY), China Petroleum Chemical Corporation (SNP), Natural Gas (NG), and New South Wales (NSW), and the training and forecasting on these data by the proposed model. In addition, some original models are selected as the comparison models and error assessment methods are used to evaluate the prediction effect of each model. Section 4 uses multiscale complexity invariant distance to evaluate the predicting performance of each model. Finally in Section 5, the conclusions and future works are stated.
Section snippets
Methodology
A main prediction system is designed. Firstly, the ensemble empirical mode decomposition (EEMD) method decomposes the original time series into different components with high and low frequency. Then a suitable prediction WNNRT model is constructed for each subseries by adjusting parameters. The predicted results of all the extracted components are combined to generate an aggregated output, and then the final predicted result is obtained. Fig. 1 shows its flow chart.
Selecting and preprocessing of the data
In this section, we pick out the energy prices series from West Texas Intermediate (WTI), Brent crude oil (BRE), Occidental Petroleum Corp. (OXY), China Petroleum Chemical Corp. (SNP), Natural Gas (NG), and New South Wales (NSW), for training to achieve the performance evaluation of the EEMD-WNNRT prediction model. Currently, there is no widely accepted method to use rigorous training data to build the best predictive model. By comparing the predicted results of samples, we choose the best
Evaluation of multiscale CID analysis
Next, using another error analysis method to more verify the accuracy of the EEMD-WNNRT model. We use the multiscale complexity invariant distance (MCID) method of analyzing multiple time scales to compare prediction results. Firstly, we introduce the Euclidean distance, which is the basis of this method. The Euclidean distance is a measure which can solve many problems well (Batista et al., 2014, Batista et al., 2011). Suppose there are two time series, and , of length
Conclusion
As the huge fluctuations in energy prices will always have an impact on the global economy, the forecast of energy prices is particularly important. In this work, a hybrid prediction model EEMD-WNNRT is constructed by adding the ensemble empirical mode decomposition to the wavelet neural network model of random time effective function. The EEMD method is used to decompose the energy price sequences to obtain different IMF components and a residual component. Then a suitable prediction model is
CRediT authorship contribution statement
Yu Yang: Conceptualization, Methodology, Investigation, Software, Visualization, Writing - original draft, Writing review & editing. Jun Wang: Conceptualization, Methodology, Investigation, Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
Authors were supported by National Natural Science Foundation of China Grant No. 71271026.
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