The global economy experienced turbulent uneasiness for the past five years owing to large increases in oil prices and terrorist’s attacks. While accurate prediction of oil price is important but extremely difficult, this study attempts to accurately forecast prices of crude oil futures by adopting three popular neural networks methods including the multilayer perceptron, the Elman recurrent neural network (ERNN), and recurrent fuzzy neural network (RFNN). Experimental results indicate that the use of neural networks to forecast the crude oil futures prices is appropriate and consistent learning is achieved by employing different training times. Our results further demonstrate that, in most situations, learning performance can be improved by increasing the training time. Moreover, the RFNN has the best predictive power and the MLP has the worst one among the three underlying neural networks. This finding shows that, under ERNNs and RFNNs, the predictive power improves when increasing the training time. The exceptional case involved BPNs, suggesting that the predictive power improves when reducing the training time. To sum up, we conclude that the RFNN outperformed the other two neural networks in forecasting crude oil futures prices.
During the past three years, the global economy has experienced dramatic turbulence owing to uneasinessbecause of terrorists’ attacks and rapidly rising oil prices. For example, the US light crude oil futures price rapidly climbed to the all-time peak about US$80 recently. Simultaneously, the US Federal Reserve continuously increased its benchmark short-term interest rates by seventeen times to prevent inflation till August 2006. Consequently, many governments and corporate managers attempted to seek a method of accurately forecasting the crude oil prices.
Accurate prediction of crude oil price is important yet extremely complicated and difficult. For example, Kumar [
The focus of this paper is to apply neural networks for predicting crude oil futures prices. This work has the following objectives: forecast crude oil futures prices using BPNs, ERNNs, and RFNNs; compare the learning and predictive performance among BPNs, ERNNs, and RFNNs, and explore how training time affects prediction accuracy.
This study classifies the previous literature into three main groups: (1) the studies that compared artificial neural networks (ANNs) with other methods to forecast futures prices, (2) the works that combined fuzzy systems with recurrent neural networks, and (3) the researches that examined the evolution or forecasting accuracy of energy futures prices.
The following studies have applied various ANNs to predict futures prices. Refenes et al. [
The following works combined fuzzy system with recurrent neural networks. Omlin et al. [
The following researches examined the evolution or forecasting accuracy of energy prices. Hirshfeld [
The paper is organized as follows. Three kinds of artificial neural networks are described in Section
As a promising generation of information processing system that expresses the ability to learn, recall, and generalize based on training patterns or data, artificial neural networks (ANNs) are interconnected assembly of simple processing nodes, whose functionality is similar to human neurons. ANNs have become popular during the last two decades for diverse applications, ranging from financial prediction to machine vision. According to Refenes et al. [
Structure of multilayer perceptron.
BPN involves two steps. The first step generates a forward flow of activation from the input layer to the output layer via the hidden layer.
The sigmoid function is usually served as
Then the gradient method is applied to optimize the weight vector of
BPNs can be widely applied to sample identification, pattern matching, compression, classification, diagnosis, credit rating, stock price trend forecasting, adaptive control, functional link, optimization, and data clustering. They can also be trained via a supervised learning task to reduce the difference between the desired and the actual outputs and have high learning accuracy. Yet BPNs have the following weaknesses: (1) slow learning speed, (2) long executing time, (3) very slow convergence; (4) falling into a local minimum of error functions, (5) lack of systematic methods in the network dynamics, (6) inability to use past experience to forecast its future behavior. This study further uses two dynamic neural networks to predict the crude oil futures prices.
Recurrent neural networks (RNNs) were first developed by Hopefield [
Refenes et al. [
Structure of the simple recurrent neural network.
According to Hammer and Nørskov [
The descriptive equations of ERNN can be considered as a nonlinear state-space model in which all weight values are constant following initialization:
Fuzzy sets theory has first been introduced by Zadeh [
Besides the fact that RNN’s underlying theory is complicated and RNN is difficult to interpret, Hu and Chang [
A structure of the recurrent fuzzy neural networks.
The information transmission process and basic functions of each layer are as follows. Input layer: the input nodes in this layer represent input variables. The input layer only transmits the input value to the next layer directly and no computation is conducted in this layer. From ( Membership layer: the membership layer is also known as a fuzzification layer and contains several different types of neurons, each neuron performs membership function. The membership nodes in this layer correspond to the linguistic label of the input variables in the input layer and serve as a unit of memory. Each of these variables is transformed into several fuzzy sets in the membership layer where each neuron corresponds to a particular fuzzy set, with the actual membership function being provided by the neuron output. Each neuron in this layer represents characteristics of each membership function, and Gaussian function serves as the membership function. The where
Each node in the membership layer possesses three adjustable parameters: Fuzzy rule layer: The fuzzy rule layer comprises numerous nodes, each node corresponds to a fuzzy operating region of the process being modeled. This layer constructs the entire fuzzy rule data set. The nodes in this layer equal the number of fuzzy sets corresponding to each external linguistic input variable and receive the one-dimensional membership degree of the associated rule from the nodes of a set in the membership layer. The output of each neuron in the fuzzy rule layer is obtained by using a multiplication operation. The input and output for the where Output layer: the output layer performs the defuzzification operation. Nodes in this layer are called output linguistic nodes, where each node is for an individual output of the system. The links between the fuzzy rule layer and the output layer are connected by the weighting values For the where
This work uses the mean square error (MSE) method to assess the performance of three neural networks. The MSE is calculated as the average of the sum of the square of the error, which is given by the difference between the actual and the designed output. MSE thus is computed as
This study focuses on energy futures for the near-month. Daily oil prices for Brent, WTI, DUBAI, and IPE are used in this investigation. The data sources are obtained from the Energy Bureau of USA and International Petroleum Exchange (IPT) of the Great Britain. This work explores the influence of training times on prediction performance so that it classifies the training period from January 1, 1990 to April 30, 2005 into three five-year sections. Table
The periods of the training patterns.
Data set | Training period | Training times (sec.) |
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I | 2000.01.01–2004.12.31. | 1244 |
II | 1995.01.01–2004.12.31. | 2499 |
III | 1990.01.01–2004.12.31. | 3758 |
This work divides the training period into three parts and uses Matlab software to perform training and testing. In order to compare the predictive power of these three artificial neural network (ANNs), the training function, namely, Levenberg Marquardt method, is employed, and the number of iterations over the data set is arbitrarily set to 1000 in order to train individual neural networks.
Table
The training times of three parts of various ANNs.
Data set | Backpropagation | Elman RNN | RNN with fuzzy | Times for each ANN |
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I | BPN1 | ERNN1 | RFNN1 | 1244 |
II | BPN2 | ERNN2 | RFNN2 | 2499 |
III | BPN3 | ERNN3 | RFNN3 | 3758 |
Following 1000 training times, Table
The comparison of the learning ability (MSE) for the three neural networks.
ANNs | Data set | MSE | ||
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I | II | III | ||
BPN |
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ERNN |
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RFNN |
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The empirical results indicate that the predictive power of the three ANNs is ranked as follows: RFNN ranks first, followed by ERNN, and finally MLP. Table
The comparison of the predictive power of the three neural networks.
ANNs | Part 1 | Part 2 | Part 3 | MSE average value |
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MLP |
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ERNN |
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RFNN |
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This study uses multi-layer perception (MLP), Elman recurrent neural networks (ERNNs) and recurrent fuzzy neural networks (RFNNs) to forecast the crude oil prices and compare the predictive power of the above three neural network models. Results of this work are summarized as follows.
All of the MSE values obtained under different training times through MLP, ERNNs, and RFNNs are below 0.0026768, suggesting that the use of the neural networks to forecast the crude oil futures prices is appropriate, and consistent learning ability can be obtained by using different training times. This investigation confirms that, under most circumstances, the more training times the neural networks take, the more the learning performance of the neural networks improves. The only exceptional case occurs at part 2 under the RFNN model, where MSE is slightly less than that obtained from part 3.
Regarding the predictive power of the three neural networks, this study finds that RFNN has the best predictive power and MLP has the least predictive power among the three neural networks. This work also finds that, under ERNNs and RFNNs, the predictive power improves when increasing the training time. However, the results are different from those obtained under MLP, indicating that the predictive power improves when decreasing the training time. Possible explanation for this phenomenon is the existence of a large difference between the predictive value and the actual value during a 9-day period. To summarize, this study concludes that the recurrent fuzzy neural network is the best among the three neural networks.
The authors would like to thank Dr. Oleg Smirnov for his insightful comments at the 81st WEA Annual Conference on July 1, 2006. Also, the authors would like to thank the anonymous referees for their valuable comments. This research is partially supported by the National Science Council of Taiwan under grant NSC 99-2410-H-033-026-MY3.