Forecasting Copper Prices Using Deep Learning: Implications for Energy Sector Economies

Abstract

Energy is a foundational element of the modern industrial economy. Prices of metals play a crucial role in energy sectors’ revenue evaluations, making them the cornerstone of effective payment management employed by resource policymakers. Copper is one of the most important industrial metals, and plays a vital role in various aspects of today’s economies. Copper is strongly associated with many industries, such as electrical wiring, construction, and equipment manufacturing; therefore, the price of copper has become a significant impact factor on the performance of related energy companies and economies. The accurate prediction of copper prices holds particular significance for market participants and policymakers. This study carried out research to address the gap in copper price forecasting using a one-dimensional convolutional neural network (1D-CNN). The proposed method was implemented and tested using extensive data spanning from November 1991 to May 2023. To assess the performance of the CNN model, standard evaluation metrics, such as the R-value, mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE), were employed. For the prediction of global copper prices, the proposed artificial intelligence algorithm demonstrated high accuracy. Lastly, future global copper prices were predicted up to 2027 by the CNN and compared with forecasts published by the International Monetary Fund and the International Society of Automation. The results show the exceptional performance of the CNN, establishing it as a reliable tool for monitoring copper prices and predicting global copper price volatilities near reality, and as carrying significant implications for policymakers and governments in shaping energy policies and ensuring equitable implementation of energy strategies.

1. Introduction

The role of copper extends beyond the market and budgeting considerations, as it also plays a vital role in energy production. Achieving sustainable development in countries heavily relies on the effective use of energy, and this critical issue should not be overlooked in the pursuit of progress. As the population increases and the use of energy continues to expand across various economic sectors, energy has become the primary driver of production. Copper’s high thermal and electrical conductivity make it an essential material for producing multiple energy-related infrastructures, such as power transmission lines, electric motors, and transformers. Therefore, the availability and efficient use of copper are essential for the development and expansion of the energy sector. Furthermore, as the world seeks alternative energy sources, such as wind and solar power, the importance of copper in the energy sector is likely to increase, making it an indispensable resource for achieving sustainable development [1].

Copper, as one of the primary industrial metals, plays a vital role in various aspects of the modern economy [1]. It is the third most widely used metal globally, following steel and aluminum, and is listed among the top metals on major foreign exchange markets, including the Commodity Exchange Market of New York (COMEX), the Shanghai Futures Exchange (SHFE), and the London Metal Exchange (LME). The price of copper is determined by the interplay of supply and demand forces, primarily on the London Metal Exchange. Copper ore is a natural resource exploited to serve a variety of purposes. Copper is mostly obtained from surface copper mines worldwide in the form of copper sulfide minerals. Chile, Peru, China, Iran, the United States, and Australia are among the largest countries that exploit and process copper [2,3,4].

Considering the special properties of copper, it is extensively used, and its alloys are widely applied in different industries, including military, construction, equipment manufacturing, electrical, automobile and machine manufacturing, electronic components, agriculture, household appliances, spiritual monuments, and musical instruments industries, etc. The complex fluctuations in the prices of copper can have a significant impact on other industries. Hence, its consumption has elevated 20-fold in less than a century [3,5].

Moreover, prices of metals are critical factors in financial models used for the evaluation of revenue, forming the foundation for efficient payment management used by resource policymakers [6]. In many economic aspects, predicting metal prices is significant. Serious fluctuations in the prices of metals in recent years have demonstrated the inability of classical estimation approaches to provide a correct estimation of volatility [1].

2. Copper Price Behaviors and Modeling

Forecasting the price of copper is crucial for several reasons. One of the key factors is that copper, along with other natural resources such as silver, is characterized by a high level of thermal and electrical conductivity. Copper’s price is lower than silver’s, and it has a higher resistance to corrosion. Hence, it is the ideal metal choice for electronic and electrical uses, both in domestic areas and in more general applications in industries. Considering the significance of telecommunication and construction sectors in modern economies, it is possible to perceive fluctuations in copper’s price as an early index of global economic performance, which significantly affects related companies’ performances. The price of copper has a significant impact on the prices of other metals. Additionally, for some developing nations, such as Zambia and Chile, which rely heavily on copper production, fluctuations in copper prices can have a significant impact on their national incomes. Chile, the world’s leading producer and exporter of copper, produced an estimated 5.6 million metric tons of copper in 2019. In 2000, the Chilean government made copper the primary reference point for its structural budget rule in an effort to reduce the country’s exposure to fluctuations in copper prices that affect its GDP [1,6].

In addition to copper’s price, critical information is provided to participants of financial markets, e.g., investment funds and banks, because they are active actors in future metal markets [6]. This denotes the intricate development of future copper prices that have a significant impact on many economies and industries of nations. Hence, precise prediction of long-term copper prices is highly important for mining enterprises, policymakers, investors, and other related industries [3].

The accurate prediction of copper prices is especially crucial for market participants and policymakers. Mining firms, in particular, rely on sound budgeting practices due to the long payback periods associated with mining projects. A dependable financial model is required to make adequate evaluations and forecasts of future costs and revenues, ensuring a strong cash flow during the project phase. Additionally, a reliable financial model is necessary for authorities granting mining licenses to assess projected revenues and determine appropriate payments or royalties from contractors. These payment regimes are established based on the models used. Given the direct relationship between copper prices and projected revenues, and their role as a critical parameter in financial models, policymakers require precise forecasts of copper prices to make informed decisions in the long run.

Furthermore, the accurate prediction of long-term copper prices holds significant importance for mining enterprises, policymakers, investors, and other related industries. Precise forecasts enable mining companies to plan their operations effectively, optimize their resource allocation, and make informed investment decisions. Policymakers rely on accurate price predictions to formulate appropriate regulations and policies that promote sustainable development and ensure the stability of the mining sector. Investors can use reliable price forecasts to assess potential risks and returns associated with copper-related investments, enabling them to make well-informed financial decisions. Moreover, other industries and economies heavily dependent on copper, such as the construction and manufacturing sectors, benefit from precise long-term price predictions as they can strategically manage their supply chains, production costs, and pricing strategies. Therefore, the precise prediction of copper prices has far-reaching implications, extending beyond the mining sector, and plays a vital role in ensuring the stability and prosperity of numerous industries and economies worldwide.

The primary motivation for using a one-dimensional convolutional neural network (1D-CNN) to forecast copper prices was to address the inherent limitations of traditional statistical models. Conventional methods such as ARMA, ARIMA, and GARCH assume linear data transformations, which can be inadequate for capturing the complex and non-linear nature of time-series data. These models often fall short in predicting the dynamic and volatile behavior of commodity prices, including copper, due to their reliance on linear assumptions and simpler pattern recognition.

CNNs, particularly 1D-CNNs, have demonstrated exceptional capabilities to recognize intricate patterns and relationships within sequential data. This makes them well-suited for time-series forecasting tasks. By employing a 1D-CNN, our approach leveraged these strengths to improve the accuracy and robustness of copper price predictions. The network’s ability to process large datasets and identify subtle patterns that influence price movements is critical in providing reliable forecasts.

Furthermore, the integration of diverse predictor variables, including the historical prices of copper, other selected metals, and crude oil, enhanced the model’s ability to account for multiple factors that affect copper prices. This multi-faceted approach ensures a more comprehensive analysis and prediction, aligning with the needs of stakeholders in the energy and commodities sectors who require precise and reliable forecasts for strategic planning and decision-making.

Our motivation was also driven by the need to advance current forecasting methodologies. Although various studies have applied CNNs to predict metal prices, our customized implementation specifically tailored to copper price forecasting, coupled with a unique dataset spanning over three decades, sets our work apart. By demonstrating superior performance in comparison to traditional methods and existing machine-learning models, our approach highlights its practical applicability and effectiveness, contributing valuable insights to the field of economic forecasting.

Moreover, this paper introduces an artificial intelligence approach to forecast copper prices using a one-dimensional convolutional neural network (1D-CNN). Although previous studies have explored various methods, such as statistical models and machine-learning algorithms, to predict copper prices, the application of 1D-CNN in this context is a pioneering contribution. Convolutional neural networks have shown remarkable success in several tasks [7,8,9,10,11,12], but their potential in financial forecasting, particularly for copper prices, remains largely unexplored. By leveraging the power of deep learning and its ability to capture complex patterns and relationships in data [13], the proposed 1D-CNN model offers a unique and promising solution to improve the accuracy of copper price prediction. This innovative approach fills a gap in the existing literature and represents a significant advancement in the field of copper price forecasting, setting a new benchmark for future research in this domain.

3. Applications of Deep Learning for Predicting Copper Prices

Generally, an input layer, a fully connected layer, a convolutional layer, an output layer, an activation function layer, a pooling layer, and a flatten layer are included in a CNN’s basic architecture. Convolutional layers mainly function to extract input spectra features [14]. For example, the first convolutional layer is considered as the convolutional layer with N same size filters. Input spectra are converted to N feature maps, followed by the convolutional layer. Nevertheless, the convolution is a linear operation. Feature maps pass through an activation function layer to run nonlinearity transformation in the network. Sigmoid function, exponential linear units (ELUs), and rectified linear units (ReLUs) are common functions. The pooling layer is mainly aimed to decrease the dimensionality of convolutional layer feature maps and prevent overfitting, thus incrementing the calculation speed. The completely connected layer is a multi-layer perceptron, where each neuron is linked to all the elements in the former layer [15].

4. Densely Connected Layer

The fully connected layer (FC layer) is another term for the layer that linearly maps the input vector into another. Neurons between adjacent layers are paired. A convolutional layer convolves a specific filter with the inputs, and the filter is spatially moved across spectra. The filter’s dot product is calculated with a local spectra window, with a stride of one, and input spectra are padded to maintain the same size as inputs and outputs. The convolutional layer typically follows fully connected layers, as illustrated in Figure 1.

Classical preprocessing techniques, such as detrend and Savitzky–Golay derivatives, can be replaced by a suitably trained convolutional layer in spectroscopic calibration to shift the weighted mean of input spectra. Instead of manually selecting a specific preprocessing technique, the optimization algorithm is used to find the most effective filter. As input vectors have 1D spectra, the filter is also a 1D vector, and the filter bandwidth is related to the input spectra resolution. Multiple parallel convolutional channels can be implemented to increase model flexibility, but a sufficient number of training samples are needed to adjust multiple convolutional filters. In this study, only a single channel (one convolutional layer) was considered for simplicity [14].

5. Activation Functions

The activation function was applied to outputs of every hidden layer to introduce nonlinearity, including both convolutional and fully connected layers. In this context, we refer to the output as y and the activation function as x.

The sigmoid function computes the element-wise sigmoid of x, given by:

$$y={\displaystyle \frac{1}{1+\mathrm{e}\mathrm{x}\mathrm{p}(-x)}}$$

(1)

The sigmoid function has been widely used due to its good biological interpretations. However, it can lead to the vanishing gradient problem when the neurons are saturated. This occurs because the gradient flow during back-propagation approaches zero when x is far from zero. Additionally, the sigmoid function is not zero-based, which makes parameter updates inefficient. The hyperbolic tangent of x element-wise is computed by the tanh function as:

$$y=\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(x\right)$$

(2)

Zero-centering can be achieved by squashing the output into the range of [−1, 1]. However, this does not solve the vanishing gradient issue.

Rectified linear units (ReLUs) perform element-wise rectification of the input, setting all negative input values to zero. The output y is defined as:

$$y=\left\{\begin{array}{c}x, x\ge 0\hfill \\ 0, otherwise\hfill \end{array}\right.$$

(3)

The ReLU activation function is known for its non-saturating nature and faster convergence compared to tanh and sigmoid functions [16]. However, it suffers from the “dead ReLU” problem, where negative inputs always result in zero outputs, potentially due to a bad learning rate or initialization of the model [17].

To address this issue, exponential linear units (ELUs) were introduced. ELUs are similar to ReLUs, except the negative section is exponential rather than zero. This allows ELUs to achieve zero-mean activations and faster convergence than ReLUs, with the added benefit of not suffering from the “dead ReLU” problem. The ELU function is defined as:

$$y=\left\{\begin{array}{c}x, x\ge 0\hfill \\ \exp \left(x\right)-1, otherwise\hfill \end{array}\right.$$

(4)

ELUs share many advantages with ReLUs, but without the “dead neuron” issue. This is because the near zero-centered output facilitates efficient weight updates, and it has a negative saturation regime that makes it robust against some noise [17]. However, one minor drawback is that the computation of exp(x) can be slow, particularly for larger networks.

6. Regularization

The model has more parameters than observations, making regularization essential to prevent overfitting. L2 regularization is commonly used in many machine-learning frameworks.

L2 regularization encourages the model to use all neurons by penalizing the sum of the squared amplitudes of the weights in the model via  ${\displaystyle \frac{1}{2}}$λ$w^2$ (where w is the weight and λ is the regularization parameter). The L2 regularization gradient is λw, which means that every weight is gradually pushed towards zero, while retaining its current sign.

Dropout is an effective method for preventing overfitting in neural networks. During training, a proportion of neurons in fully connected layers are randomly activated, and the parameters of the selected neurons are updated. Dropout is not used during testing. Although dropout is simple, it is effective and widely used in modern practical neural networks. The principle and connection of dropout have been recently explained [18,19], along with other regularization techniques.

The objective of this paper is to use a convolutional neural network to predict copper prices. The proposed algorithm’s effectiveness was measured using mean squared error (MSE), mean absolute error (MAE), root mean squared error (RMSE), and correlation coefficient (R) between the output of the CNN and the actual dataset [20], which are defined by Equations (5)–(7):

$$\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n{(y_{observed}^i-y_{predicted}^i)}^2$$

(5)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\mathrm{ǀ}{y}_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}^i-y_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}}^i\mathrm{ǀ}$$

(6)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^{\mathrm{n}}{(y_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}^i-y_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}}^i)}^2}$$

(7)

where $y_{\mathrm{i}}$ (copper price) is the ith observed value, ${\widehat{y}}_i$ is the corresponding predicted value for${ y}_{\mathrm{i}}$, and n is the number of observations.

The first step to obtain copper price data is normalization, and Equation (8) is used for this purpose [21].

$$X_N={\displaystyle \frac{\left(X_R-X_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}\right)}{\left(X_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}-X_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}\right)}}$$

(8)

Here, X_N represents the normalized value, X_R is the value to be normalized, X_minimum is the minimum value in all values for related variables, and X_maximum is the maximum value in all values for related variables. X_minimum and X_maximum values for each variable are selected time series of monthly prices from November 1990 to September 2021 (359 monthly samples), and are presented in

Table 1. Minimum and maximum values of research variables used for normalization.

Variable	Maximum	Minimum
Silver (USD per troy ounce)	42.7	3.65
Aluminium (USD per metric ton)	3071.24	1039.81
Nickel (USD per metric ton)	52,179.05	3871.93
Gold (USD per troy ounce)	1968.63	256.08
Iron (USD per dry metric ton)	214.43	26.47
Coal (USD per metric ton)	185.69	22.25
Crude Oil price (USD per barrel)	132.83	10.41
Copper (USD per metric ton)	10,166.29	1377.376

.

The selection of input variables for our model was based on an extensive literature review to ensure a comprehensive approach to forecasting copper prices. We used overlapping moving windows to preserve time series features, allocating 20% of the most recent data within each window as test data and the remaining 80% for training and validation to preserve the time series trend [22]. Variables included prices of silver, aluminum, nickel, gold, iron, coal, and crude oil, and the global copper price itself. These variables were chosen due to their significant impact on copper prices, as identified in previous studies. Notable references that informed our selection include Astudillo et al. [1], Liu [5], Zhang et al. [3], and Khoshalan [6], among others. The chosen variables provided a robust dataset that enhanced the accuracy of our forecasting model. Table 1 presents the minimum and maximum values of these research variables used for normalization.

7. Results and Discussion

In this study, a convolutional neural network (CNN) was used to estimate the global price of copper based on various input variables, such as silver, aluminum, nickel, gold, iron, coal, and crude oil prices. To ensure a robust evaluation of the CNN model’s performance, we utilized monthly data for training and testing. The dataset was divided into training and test sets by splitting data sequentially, maintaining time series characteristics. Specifically, 80% of the most recent data was used for training and validating, while the remaining 20% was allocated for testing. Regarding annual forecasts used for comparison with the IMF and ISA, we converted the monthly forecasts generated by our CNN model into annual forecasts by averaging the monthly predicted values for each year. This approach was intended to demonstrate the model’s accuracy against established benchmarks. Figure 2 displays the performance of the CNN for the training and testing data sets, indicating that the model’s errors significantly decreased over the learning process (epochs). The process epochs reached 1000, and the error rate was reduced to less than 0.1, demonstrating the model’s ability to produce information with low error. After completing the learning process, the CNN model demonstrated high accuracy with an R-value of 0.98, MSE of 0.0337, MAE of 0.119, and RMSE of 0.1835. The error function is frequently used to evaluate a predictive model’s performance [23,24].

The analysis revealed that for 1000 epochs, the estimated values for MAE and RMSE were approximately 0.119 and 0.183, respectively. The decrease in MAE and RMSE values indicates that the method has a high prediction accuracy.

The performance of the CNN method is illustrated in Figure 3 for both training and testing datasets. To provide an accurate comparison, both forecasted values and actual data are depicted in their original scale.

In this study, we employed a convolutional neural network (CNN) method to forecast global copper prices up to the year 2027. The CNN model’s predictions were compared with forecasts published by the International Monetary Fund (IMF) and the International Society of Automation (ISA), as shown in

Table 2. A comparison of projections of global copper prices for the years 2023–2027.

Year	CNN	ISA	IMF
2023	8563	8930	10,048
2024	8381	8472	9908
2025	8882	8640	9751
2026	9376	8853	9629
2027	9890	8998	9584

. This comparison underscores the CNN method’s effectiveness in predicting future copper prices, offering a promising tool for analysts and investors in the commodities market.

The comparative analysis evaluated the predictive accuracy of our method against various other approaches, including multi-layer perceptron (MLP) neural networks [3], least absolute shrinkage and selection operator (LASSO), gradient boosting decision tree (GBDT), extreme gradient boosting (XGBoost), random forests (RF) [25], sparrow search optimization (SSO) with XGBoost [26], ensemble methods [27], LSTM [28], ANN [6], different tree approaches [25], ARIMA [29,30], and exponential smoothing [31].

8. Conclusions

This study addressed the gap in copper price forecasting by employing a one-dimensional convolutional neural network (1D-CNN). Our approach aimed to enhance the accuracy of global copper price predictions by incorporating various influential factors, including prices of silver, aluminum, nickel, gold, iron, coal, crude oil, and the global copper price itself. The performance evaluation of the CNN model was conducted using mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE) metrics, comparing the model’s output with the actual dataset. The results unequivocally demonstrate the reliability and effectiveness of the proposed CNN model for copper price prediction. The insights gained from this research have significant implications for policymakers and energy system developers. The proposed method can contribute to the development of robust energy plans and facilitate accurate modelling of energy systems. Moreover, it serves as a reliable instrument for governments and policymakers to effectively monitor and regulate energy programs, enabling informed economic interventionism by the government. Overall, our innovative approach holds the potential to establish a level playing field for assessing the impact of energy policies on the energy structure, fostering informed decision-making in the energy sector.