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Resources Policy 78 (2022) 102906
Available online 5 August 2022
0301-4207/© 2022 Elsevier Ltd. All rights reserved.
Medium- to long-term nickel price forecasting using LSTM and 
GRU networks 
Ali Can Ozdemir a,*, Kurtuluş Buluş b, Kasım Zor c 
a Department of Mining Engineering, Çukurova University, Adana, 01330, Turkey 
b Centre for Discovery Brain Sciences, University of Edinburgh, Edinburgh, UK 
c Department of Electrical and Electronic Engineering, Adana Alparslan Türkeş Science and Technology University, Adana, Turkey 
A R T I C L E I N F O 
Keywords: 
Nickel price forecasting 
LSTM networks 
GRU networks 
Recurrent neural networks 
Deep learning 
A B S T R A C T 
Recently, nickel is a critical metal for manufacturing stainless steel, rechargeable electric vehicle batteries, and 
alloys utilized in the state-of-the-art technologies. The use of more environmentally friendly electric vehicles has 
become widespread and brought tackling climate change to forefront, especially for reducing greenhouse gas 
emissions. Therefore, the demand for rechargeable batteries that power electric vehicles and the need for the 
nickel in the production of these batteries will increase as well. In addition to those, nickel prices significantly 
impact mine investment decisions, mine planning, economic development of nickel companies, and countries 
that depend on nickel resources. However, there is uncertainty about how the nickel price will trend in the 
future, and the solution to this problem attracts the attention of researchers. For forecasting nickel price, this 
paper proposes recurrent neural networks-based on long short-term memory (LSTM) and gated recurrent unit 
(GRU) networks, classified as deep learning algorithms. Mean absolute percentage error (MAPE) was used as the 
performance measure to compute the accuracy of the proposed techniques. As a result, it has been determined 
that the LSTM and GRU networks are very useful and successful in forecasting the nickel price variations owing 
to having average MAPE values of 7.060% and 6.986%, respectively. Furthermore, it has been observed that GRU 
networks surpassed the LSTM networks by 33% in terms of average computational time. 
1. Introduction 
In recent years, nickel has been a crucial and strategic metal for 
developing and modern societies. High resistance to corrosion and 
tarnishing are some of the most important advantages of nickel in 
comparison with other metals. Thus, it is widely used in many industries 
such as household appliances, automotive, aerospace, military applica-
tions, coin making, and computer parts manufacturing (British 
Geological Survey, 2008, 2018; Nickel Institute, 2019; Henckens and 
Worrell, 2020). In particular, its use in stainless steel, alloys, and 
rechargeable batteries significantly contributes to the economic growth 
and development of any country (Eckelman, 2010; Yan et al., 2012; 
Schmidt et al., 2016; Liu et al., 2017; Wang et al., 2018). 
In parallel with the rapid development of the global economy, 
releasing large amounts of greenhouse gas (GHG) emissions to the at-
mosphere has led to a dramatic increase in the global warming which 
causes the climate change (Fu et al., 2021). Several multinational 
agreements have been signed by the international community to 
struggle with this problem. Herein, some examples can be stated as the 
United Nations Framework Convention on Climate Change, the Kyoto 
Protocol, the Paris agreement, the Europe 2020 strategy, the 2030 en-
ergy policy framework vision, and the European Green Deal (Tunç et al., 
2007; Karmellos et al., 2021). The common purpose of these actions is to 
combat both the global warming and the climate change on a global 
scale. For this purpose, the focus has been concentrated on reducing 
carbon dioxide (CO2) emissions, which are the biggest contributors to 
GHG emissions (Fukuzawa, 2012; Wang and Wang, 2019; US Environ-
mental Protection Agency, 2022). CO2 emissions originating from 
transportation sector constitute 25% of total CO2 emissions and it is the 
second sector that produces the most CO2 emissions after electricity 
generation (IEA, 2022). At this point, electric vehicles (EVs) have great 
potential to meet the goal of reducing CO2 emissions within the trans-
portation sector (Ma et al., 2019; McCollum et al., 2018). Between 2022 
and 2025, it is expected that EVs will be able to compete with traditional 
vehicles in terms of cost, range, and infrastructure criteria, and they will 
be collectively adopted (Baker et al., 2019; Woodward et al., 2019; 
* Corresponding author. 
E-mail addresses: acozdemir@cu.edu.tr (A.C. Ozdemir), s1834500@ed.ac.uk (K. Buluş), kzor@atu.edu.tr (K. Zor). 
Contents lists available at ScienceDirect 
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https://doi.org/10.1016/j.resourpol.2022.102906 
Received 20 February 2022; Received in revised form 16 July 2022; Accepted 18 July 2022 
mailto:acozdemir@cu.edu.tr
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Bloomberg New Energy Finance, 2021). It has been also predicted that 
the annual sales of EVs may be between 21 and 28 million in 2030 
(Cooper and Schefter, 2018; IEA, 2019). Moreover, aggressive thinkers 
estimate that this number may reach 43 million (Azevedo et al., 2018; 
IEA, 2019). 
From a technical point of view, nickel is an essential metal in the 
production of EVs batteries due to its low-cost and high energy density 
compared to its equivalents (Roskill Information Services Ltd, 2017; Li 
and Lu, 2020; Nguyen et al., 2021; Yao et al., 2021). Elon Musk, CEO of 
Tesla, which has become the most popular brand in the automobile in-
dustry, emphasizes the importance of nickel for the battery re-
quirements of EVs at every opportunity (Electrek, 2022). Also, Hamilton 
(2018) stated that the use of nickel in batteries for EVs will increase by 
39% annually between 2017 and 2025. The share of global nickel con-
sumption in the battery industry is estimated to increase from 3% in 
2017 to 37% in 2030 (Yao et al., 2021). If this momentum continues, it is 
forecasted that nickel demand in 2030 will be roughly one and a half 
times of global nickel production in 2017 (British Geological Survey, 
2018; BMO Capital Markets, 2018). It was observed that the world 
nickel production increased by 3.1% annually between 1980 and 2015 
(US Geological Survey, 2021). Henckens and Worrell (2020) stated that 
when the average production increase rates in this period are adjusted to 
the year 2100, nickel production in 2100 will be twelve times higher 
than the nickel production in 2018. These observations indicate that 
there will be an increase in the production of batteries as well as EVs. In 
summary, it is clarified that nickel needs of EVs battery manufacturers 
have been increasing and will continue to rise in the future. 
It is a known fact that fluctuations in metal prices can have a sig-
nificant impact on both microeconomics and macroeconomics (Wang 
et al., 2019; Khoshalan et al., 2021). These fluctuations have major in-
fluences especially on the countries whose metal export income consti-
tutes a large part of the total export income (He et al., 2015). In addition, 
for metal producing companies, it is a situation that requires great 
attention in the execution of mining activities, the preparation of short- 
and long-term plans, cost analysis, and risk management (He et al., 
2017; Bhatia et al., 2018; Gong and Lin, 2018). It is considered that 
metal price is at the center of mining activities, understanding future 
metal price tendency is vital(Chatterjee and Dimitrakopoulos, 2020; 
Madziwa et al., 2022). Abdel Sabour (2002) stated that if prices are 
predicted to increase, production will increase; on the contrary, if prices 
are predicted to decrease, production will decrease. Here, the impor-
tance of price forecasting for mine planning is emphasized once again. 
Unsuccessful nickel price forecasts can increase the likelihood of errors 
in economic assessments and result in large financial losses on in-
vestments (Hatayama and Tahara, 2018). Therefore, nickel price fore-
casts should be done by employing a method with high accuracy. Thus, 
it will provide important contributions to nickel producers, such as the 
mine planning, directing investments correctly, using resources effi-
ciently, and increasing profitability as much as possible (Cheng et al., 
2015; Liu and Li, 2017). 
Meanwhile, Hong and Fan (2016) divided forecasting process into 
four groups according to their horizons: very short-term forecast (VSTF), 
short-term forecast (STF), medium-term forecast (MTF), and long-term 
forecast (LTF). Here, the cut-off horizons are one day, two weeks, and 
three years, respectively. 
The main objective of this study is to propose RNN-based deep 
learning techniques, namely, LSTM and GRU networks for forecasting 
nickel prices in the medium- to long-term horizon. Within the scope of 
the study, a data set containing monthly commodity prices of eight 
metals (nickel, aluminum, copper, gold, iron, lead, silver, and zinc) 
between March 1991 and May 2021 was created along with introducing 
calendar variables. The validity of the proposed methods was tested on 
this data set. 
The original contributions of this study to the literature are mainly 
reflected in several aspects: 
(i) At least to one’s knowledge, this study presents the first research 
in which nickel price forecasting has been performed by using 
LSTM and GRU networks. These networks were proven for 
robust, efficient, and reliable forecasting results for other pre-
diction problems (Liu et al., 2020; Li et al., 2022). However, their 
implementations were not accomplished for nickel price 
forecasting. 
(ii) In this study, nickel price forecasting was carried out for the 
medium- to long-term horizon. The data set consists of nickel, 
aluminum, copper, gold, iron, lead, silver, and zinc prices for the 
period between March 1991 and May 2021. 
(iii) Both LSTM and GRU networks were implemented by incre-
menting the number of neurons in the hidden layer by 25 from 
200 to 400, and the number of epochs by 25 between 50 and 150 
as well. Hence, it produces findings on the question of how the 
change in the number of neurons and epoch number in the hidden 
layer affects the forecast accuracy and computational time. 
(iv) This study can be a solution to the problem of nickel price un-
certainty in the mining industry, thereby increasing reliability in 
the preparation and implementation of mining plans. 
(v) This study also encourages researchers to predict commodity 
prices for other critical resources (i.e gold, copper) using the 
proposed methods. 
The rest of this paper is organized as follows: the literature review is 
given in Section 2. The data set and forecasting methods are described in 
Section 3. The forecast results from the proposed LSTM and GRU net-
works and discussion are presented in Section 4. Finally, conclusions are 
provided in Section 5. 
2. Literature review 
Over the last few decades, forecasting metal prices has remained 
popular, and many researchers have applied different techniques to 
improve the forecasting accuracy of metal prices. For example, Brunetti 
and Gilbert (1995) conducted a study on the volatility of metal prices 
and developed a model that relates the volatility of metals to metal 
balance. The findings indicated that volatility showed no tendency to 
increase over the period 1972–1995 for the six London Metal Exchange 
(LME) metals such as nickel, aluminum, copper, lead, tin, and zinc. 
Panas (2001) researched into price behavior in the London Metal Ex-
change (LME) and tested long memory and chaos analyses on the same 
six metals to evaluate the behavior of metal prices. The results of the 
study showed that the dynamics of the LME can be attributed to long 
memory, short memory behavior, anti-persistent, and deterministic 
chaotic processes. Cortez et al. (2018) proposed a model combining 
chaos theory and a machine learning approach. It was emphasized that 
both methods cannot be used alone and must work together to predict 
long-term prices. 
Dooley and Lenihan (2005) applied autoregressive integrated mov-
ing average (ARIMA) to predict monthly metal prices. The conclusions 
of the study revealed that price forecasting is a tedious challenge and 
ARIMA provides better forecast performance than the lagged forward 
price. Behmiri and Manera (2015) investigated the role of outliers and 
oil price shocks on the volatility of metal prices using the generalized 
autoregressive conditional heteroskedastic and the glos-
ten–jagannathan–runkle models. It was found that outliers bias the 
estimation models, and the price volatility of metals reacts differently 
and asymmetrically to oil price shocks. Chen et al. (2015) evaluated the 
performance of the modified grey wave forecast model by using monthly 
prices of nickel and zinc belonging to the year 2015. Chen et al. (2016) 
built a new grey wave model for the prediction of nickel and aluminum 
prices. The results of these two studies demonstrated that the modified 
grey wave method is better than the original grey wave method in terms 
of prediction accuracy and computational efficiency. 
Fernandez (2018) measured price and income elasticity using the 
A.C. Ozdemir et al. 
Resources Policy 78 (2022) 102906
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Divisia-moment approach for eight geographic regions and seven major 
metals (nickel, aluminum, copper, lead, steel, tin, and zinc). The study 
unveiled that South America’s per capita consumption of steel, 
aluminum, and copper is the most price-elastic, and for nickel 
price-elastic regions are North America, Africa, Oceania, and the Middle 
East. Brown and Hardy (2019) showed that the Chilean exchange rate 
can predict returns on the LME and the same six metals. The results of 
the study indicated that the Chilean peso is heavily affected by the 
fluctuations in the copper price. Drachal (2019) used various Bayesian 
model combination schemes based on dynamic model averaging to 
forecast lead, nickel, and zinc spot prices based on monthly data from 
1996 to 2017. The findings of the study proved that analyzed model 
combinations produce successful prediction results. Olafsdottir and 
Sverdrup (2021) evaluated the sustainability of long-term nickel supply 
using the WORLD7 model. In the study, an estimate of the nickel price 
between 2000 and 2020 was carried out. The results demonstrated that 
for nickel, extraction rates will reach their maximum in 2050, and most 
primary nickel resources will be depleted by 2130. Madziwa et al. 
(2022) utilized the autoregressive distribution lag (ARDL) model to 
forecast annual gold prices. Then, in the study, the model that provides 
the best ARDL estimation results was encountered with the stochastic 
mean conversion and ARIMA methods. The ARDL model was deter-
mined to be the best forecasting method to predict annual gold prices. 
Shao et al. (2019) proposed a model based on an improved particle 
swarm optimization (PSO) algorithm combined with LSTM networks for 
the prediction of nickel price. The improved PSO-LSTM model was 
compared with the traditional LSTM networks and ARIMA. The results 
showed that the improved PSO has a faster convergence rate and can 
effectively improve the prediction accuracy ofthe LSTM networks. 
Alameer et al. (2019) proposed a hybrid model integrating the whale 
optimization algorithm (WOA) and the multilayer perceptron neural 
networks (NN) for forecasting gold price fluctuations. The proposed 
model compared with other models, including the classic NN, PSO for 
NN, genetic algorithm for NN, and grey wolf optimization for NN. In this 
study, it was concluded that the hybrid WOA-NN model was superior to 
other models. Khoshalan et al. (2021) applied four different forecasting 
models to predict the price of copper such as gene expression pro-
gramming, NN, adaptive neuro-fuzzy inference system (ANFIS), and a 
combination of ANFIS and ant colony optimization algorithm. The NN 
model showed the best performance among the applied models. Gu et al. 
(2021) proposed a hybrid approach based on gradient boosting decision 
tree, correlation analysis, and empirical wavelet transform, and applied 
it to predict the nickel consensus price of the LME. The findings illus-
trated that the EWT–GBDT can achieve the best results. 
Liu et al. (2022) introduced a hybrid NN with Bayesian optimization 
and wavelet transform to forecast the copper price in both short- and 
long-term horizons. Also, LSTM and GRU networks are utilized to train 
the data and predict future copper prices. The results emphasized that 
both LSTM and GRU networks can be employed for predicting copper 
prices in the short- and long-term horizons. 
3. Material and methods 
This section defines the data set in detail as the material and briefly 
explains the RNN-based LSTM and GRU networks as forecasting 
methods. 
3.1. Material 
3.1.1. Data set information 
The data set used in this study includes the historical data of metal 
prices for a period of 30 years from March 1991 to May 2021. The data 
set period covers the global financial crisis of 2008, the European debt 
crisis period of 2009–2014, the oil price crash of 2014–2015, and the 
ongoing COVID-19 pandemic. Thus, the analysis of the effects resulting 
from such major events has been enabled. Monthly price data for eight 
metals, namely nickel (Ni), aluminum (Al), copper (Cu), gold (Au), iron 
(Fe), lead (Pb), silver (Ag), and zinc (Zn), was downloaded from 
IndexMundi and demonstrated in Fig. 1. 
3.1.2. Descriptive statistics of data set 
The descriptive statistics of the data set are reported in Table 1. The 
average value, which the data in a data set are gathered, is expressed as 
the mean. The measure of spread, which represents the spread of vari-
able values around the mean, is the standard deviation (SD). Since the 
mean values of all variables are larger than the SD values, it is under-
stood that they show a spread close to the mean. To indicate a normal 
distribution according to Desgagné and de Micheaux (2018), the skew-
ness (SK) and kurtosis (KU) values of a data set should be in the range of 
[− 1,+1] and [− 2,+2], respectively. It has been found that nickel has a 
relatively large kurtosis value of 4.80 and therefore showed a sharpness 
within the normal distribution. It can be interpreted that other input 
variables show a distribution close to normal. 
The correlation chart describing the relationship between all vari-
ables is illustrated in Fig. 2. Pearson’s correlation showed that nickel had 
the highest correlation of 0.85 with Al and the lowest correlation of 0.47 
with Au among all inputs. In addition, it was understood that there was a 
generally significant relationship between other variables. 
3.2. Forecasting methods 
Prediction of the future price of properties such as metals, which are 
heavily influenced by global market demands, is an arduous task. The 
fluctuations caused by various dynamics make the data complex and 
volatile. Hence, the development of a model that predicts the future 
quantity must consider such complex factors to provide robust fore-
casting results. 
There are many machine learning models which are used for fore-
casting purposes. Earlier approaches require a large amount of time for 
preprocessing of the data. Achievement of these processes is such a 
significant step that there is a dedicated title, feature engineering, that 
was given to it. Feature engineering simply corresponds to the trans-
formation of the raw data to improve the prediction of the corre-
sponding forecasting model. In time series forecasting, this step involves 
the removal of unnecessary information which associates with the se-
lection of useful features and transforming them into another mathe-
matical form. 
Although classical machine learning models yielded robust, efficient, 
and high-accuracy outcomes for forecasting problems, their imple-
mentations often require a considerable amount of expertise for expe-
rienced users to realize feature engineering. Recent efforts in machine 
learning to automate the feature extraction steps led to the development 
of deep learning. In this new frontier, feature engineering is not required 
and the prediction is made by direct utilization of the raw data by 
feeding the raw data into various types of NN (Goodfellow et al., 2016). 
In terms of time series data, RNNs are the most common methods in deep 
learning. In RNN, the data are processed as a sequence and each time 
point is fed into the cells where the patterns of the data are captured. 
These patterns are called cell memory and they are transferred to the 
next points by using mathematical equations. The prediction of the 
interesting quantity is then accomplished after the network is fitted to 
the corresponding data by using sophisticated learning algorithms. 
Although basic RNNs are capable of dealing with time series forecasting, 
their implementation poses a significant challenge in backpropagation 
due to vanishing or exploding gradient problems (Hu et al., 2018). 
To solve the aforementioned problem, LSTM networks were pro-
posed in the late 1990s (Hochreiter and Schmidhuber, 1997; Buluş and 
Zor, 2021). Since then LSTM networks set the standard for many prob-
lems in time series forecasting and some similar approaches are devel-
oped. Recently, one of the variants of the LSTM networks, which is 
called the gated recurrent unit (GRU) network, was developed and 
attracted lots of interest due to its computationally efficient structure 
A.C. Ozdemir et al. 
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4
(Cho et al., 2014; Zor and Buluş, 2021). These networks use fewer re-
sources as well as provide better accuracy compared to LSTM networks. 
Modern machine learning methods are working horses of many 
forecasting problems. In machine learning, the forecasting process is 
achieved in 3 steps; data preprocessing, model construction, and 
training of the model to fit the data. In the data preprocessing step, a 
matrix X, which has NxM dimensions, is defined. Here N represents the 
number of observation which corresponds to each time point for time 
series forecasting problem and M is the number of features which affect 
the prediction of interested quantity. Each column in this matrix is called 
as a feature vector. Since each feature might have different scales, this 
matrix is normalized in order to prevent the prediction unbiased to the 
feature which has higher or lower scales. The mathematical form of 
feature matrix has significant effect on the prediction performance of the 
model. Hence, in machine learning, but not in deep learning, the feature 
space might be transformed to another mathematical form to obtain the 
maximum of information from the data set. This process is often referred 
as feature engineering. Once preprocessing is completed and relevant 
features are extracted, a mathematical model is then constructed. The 
mathematical model defines the rules of the relationship betweeninput 
variables and predicted output variables. A sea of mathematical models 
is available in machine learning literature and each has their own 
assumption. Unfortunately, there is no single model that can work 
effectively on every prediction problems. This is called as no free lunch 
theorem in machine learning. Hence, it is often suggested to apply a set 
of machine learning models to the interested problem and pick the one 
that yields the best performance metrics. The generic equation of the 
model to make a prediction is given below: 
Fig. 1. IndexMundi monthly price data for eight metals (Wickham, 2016). 
Table 1 
The descriptive statistics of data set. 
Metal Min Max Median Mean SD SK KU 
Ni ($/t) 3871.93 52179.05 11118.29 12878.39 7635.90 1.83 4.79 
Al ($/t) 1039.81 3071.24 1709.27 1767.19 428.64 0.80 0.19 
Cu ($/t) 1377.28 10161.97 4269.34 4493.01 2500.95 0.29 − 1.38 
Au ($/ounce) 256.08 1968.63 585.78 802.53 510.86 0.52 − 1.21 
Fe ($/t) 26.47 207.72 58.05 70.19 47.92 1.05 0.02 
Pb ($/t) 375.70 3719.72 1124.08 1328.52 793.64 0.34 − 1.21 
Ag ($/ounce) 3.65 42.70 10.29 12.34 8.63 1.05 0.55 
Zn ($/t) 747.60 4405.40 1518.00 1715.20 788.11 0.80 − 0.07 
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f (x)=w1x1 + w2x2 + … + wMxM =
∑m=M
m=1
wmxm = wTx (1) 
where xi, i = 1, 2, … M is corresponding features and wi, i = 0, 1, …, M is 
the associated weight for each feature. The model multiplies each 
feature with the corresponding weight and then sum all the values to 
obtain the target value. This process can also be described as a linear 
vector multiplication, which is stated in the above equation as wTx. w 
includes the parameters of the model which need to be fit to the cor-
responding data set. Fitting those parameters is then achieved in the 
training step by utilization of gradient descent algorithms which iterate 
each data point or group of data points over the entire training set to find 
optimal settings in the parameter space (Goodfellow et al., 2016; Bishop 
and Nasrabadi, 2006; Murphy, 2012). 
State-of-the-art forecasting methods leverage the advancements in 
deep learning due to the fact that their implementation does not require 
any feature engineering and these methods performed very well in the 
case of large data size because of their complex, yet efficient, optimi-
zation methods. Deep learning methods use deep neural networks to 
extract the hidden patterns of the data set to approximate the underlying 
mapping function between input and output variables. Backpropagation 
is the main optimization method that is utilized in deep neural networks 
to fit the parameters. However, sometimes backpropagation might pose 
a challenge. For example, RNNs also use backpropagation to optimize 
the model parameters. However, backpropagation may lead to vanish-
ing or exploding gradient problems. In order to overcome such a prob-
lem, LSTM and GRU networks were developed. 
3.2.1. LSTM networks 
To solve the vanishing or exploding gradient problems, LSTM net-
works have gating mechanisms in each cell where three different input 
types are fed into. As illustrated in Fig. 3, these are xt, ht− 1, and Ct− 1. In 
terms of the time series forecasting problems, xt represents the current 
time point, ht is the hidden state, and Ct is the cell state. 
The power of LSTM networks comes from the updating mechanisms 
of the cell state and hidden state through a set of mathematical opera-
tions. These operations allow the network to keep track of long-term 
patterns to supply reliable predictions based on historical data. 
Another important advantage of such a complex gating mechanism is to 
prevent the gradient calculation from approaching zero (vanishing) or 
infinity (exploding). The governing mathematical equations in LSTM 
networks are given as follows: 
ft = σ
(
Wf ⋅ [ht− 1, xt] + bf
)
(2) 
it = σ(Wi ⋅ [ht− 1, xt] + bi) (3) 
ot = σ(Wo ⋅ [ht− 1, xt] + bo) (4) 
Fig. 2. Correlation chart (Peterson et al., 2014). 
Fig. 3. LSTM cell structure. 
A.C. Ozdemir et al. 
Resources Policy 78 (2022) 102906
6
C̃t = tan h(Wc ⋅ [ht− 1, xt] + bc) (5) 
Ct = ft ⊙ Ct− 1 + it ⊙ tan h(Ct) (6) 
ht = ot ⊙ tan h(Ct) (7) 
where ht and Ct are hidden layer vectors, xt is input vector, bf, bi, bc, and 
bo are bias vectors, Wf, Wi, Wc, and Wo are parameter matrices, and 
sigmoid and tanh are activation functions (Buluş and Zor, 2021). 
Eq. (4) and Eq. (6) are called as input gate because these operations 
use current input and hidden state to control the usefulness of infor-
mation in the short-term. To do so, hidden state is multiplied by current 
input value and then pass through sigmoid function. The output of sig-
moid function is either one or zero, which means the information will be 
either kept or removed, respectively. Similarly, Eq. (6) uses the same 
input and pass it through the tanh activation function to regulate the 
network. The output of these two equations gives the final result for 
input gate. Eq. (2) is referred as forget gate and its main function is to 
control the information for long-term memory. Hence, the output of 
input gate is multiplied by the cell state to filter out unnecessary infor-
mation in the long-term. This multiplication is then summed with the 
second layer of the input gate to construct the updated cell state to be 
transmitted to the next cell in the network. Finally, the last gate, which is 
referred as output gate, performs a mathematical operation in Eq. (7) to 
obtain the updated hidden state. These processes is repeated in each cell 
for each time step and the output of correspondent time step can be 
obtained from the short-term memory, i.e. hidden state, ht. 
3.2.2. GRU networks 
GRU networks possess a similar cell structure to LSTM networks. 
However, their simpler gating mechanisms in comparison with LSTM 
networks allow the system to perform complex computations with fewer 
resources in a lesser amount of time. Thus, the training of these networks 
is performed at a higher speed. The cell mechanisms of GRU networks 
are depicted in Fig. 4. 
One of the main differences between GRU and LSTM networks is the 
fact that, unlike LSTM networks, GRU networks combine the cell state 
and hidden state in one variable, namely ht. The mathematical opera-
tions which allow GRU networks to accomplish the above operations are 
given as follows: 
zt = σ(Wz ⋅ [ht− 1, xt] + bz) (8) 
rt = σ(Wr ⋅ [ht− 1, xt] + br) (9) 
h’t = tan h(Wh ⋅ [rt ⊙ ht− 1, xt] + bh) (10) 
ht =(1 − zt) ⊙ ht− 1 + zt ⊙ h’t (11) 
where ht is hidden layer vectors, xt is input vectors, bz, br, and bh are bias 
vectors, Wz, Wr, and Wh are parameter matrices (Zor and Buluş, 2021). 
Eq. (8) and Eq. (9) perform the mathematical operations to receive 
inputs from previous hidden state and current data point. Once these 
inputs are processed with the corresponding weights, the output is then 
passed through non-linear activation function, tanh, to filter out un-
necessary information as stated in Eq. (10). Hence, this section of the 
network is referred as reset gate. As a final step, the network updates the 
hidden states with the set of mathematical operations, which stated in 
Eq. (11). The updated hidden state is then transmitted to the next cell. 
Throughout the training phase, these steps are repeated. 
4. Results and discussion 
Experiments regarding the deep learning architectures were per-
formed on Linux Ubuntu OS which had the NVIDIA T500 GPU. PyTorch 
(Paszke et al., 2019), an open-source machine learning libraryfor Py-
thon programming language, was utilized to implement both LSTM and 
GRU networks. Since the measurements of each feature were not on the 
same scale, the models would be biased toward the features which had 
larger observations. To prevent this problem, a scaling operation was 
performed. The scaling operation is called min-max normalization and 
the following formula was used: 
xscaled =
x − min(x)
max(x) − min(x)
(12) 
where min(x) and max(x) correspond to the minimum and maximum of 
the scaled feature vector, respectively. 
In both LSTM and GRU networks, the long sequential data, which 
have the form of a 1xD vector where the D number of time points in this 
study, must be wrapped into N xM matrix form, in which N is the number 
of rows and M is the number of columns. In this study, M was chosen as 
12, meaning that each observation is made based on the recent 12 time 
points. In most deep learning algorithms, during the training phase, the 
390 data have processed batches to ease the training. To predict the 
future nickel price, the batch was set to 5. Both models are optimized by 
using the Adam optimizer (Kingma and Ba, 2014) and the back-
propagation of the error function was performed by using the L1 loss 
function. Neural networks are prone to overfitting which causes the 
predictions to be unreliable on unseen data. To prevent the network 
from overfitting, a dropout layer was implemented and the drop out 
probability was set to 0.2. Finally, the learning parameter was set to 
0.001. 
For the validation and robustness of both algorithms, the data were 
split into two sets, namely, training sets and test sets in a random 
manner. While training sets consisted of 80% of the all data set, the test 
set formed 20% of it. To evaluate the performance results, mean abso-
lute percentage error (MAPE) was used and the calculation of the error 
was achieved based on the following formula: 
MAPE(%)=
100
n
∑n
i=1
|yi − ŷi|
|yi|
(13) 
where yi is actual output, ŷ is forecasted output, and n indicates the 
number of instances (Ozdemir, 2021). 
In the analyzes for both LSTM and GRU networks, the number of 
neurons in the hidden layer is varied between 200 and 400 by 25, while 
the epoch number is changed from 50 to 150 by 25 as well. Fig. 5 shows 
the change in MAPE and computational time for each year from 2022 to 
2031. MAPE values filtered below 10% are indicated on the x-axis, while 
the y-axis shows the computational time in seconds. When the forecast 
Fig. 4. GRU cell structure. 
A.C. Ozdemir et al. 
Resources Policy 78 (2022) 102906
7
performances are compared every year, it is observed that the best 
forecast result for both networks is obtained in 2026. In the years 2029 
and 2030, there are a few MAPE values below 10% for GRU networks, 
while there is only one MAPE value appertaining to LSTM networks. 
Therefore, it is deduced that the MAPE values belonging to the other 
years are more successful than these years in terms of accuracy. This 
circumstance can be also verified by observing Table 2 in which the 
results of the average MAPE values for these years are the highest of all 
years. 
Table 2 shows the performance results of the applied algorithms 
between the years 2022 and 2031. Although the models do not have 
significant differences in terms of average MAPE values, the average 
computational time of the GRU networks managed to reduce computa-
tional time to 33% less than LSTM networks. This is caused by the 
Fig. 5. Illustration of MAPE (%) versus computational time (s) with respect to the years between 2022 and 2031. 
Table 2 
Performance results. 
Year LSTM Networks GRU Networks 
Size&Epoch Time (s) MAPE (%) Size&Epoch Time (s) MAPE (%) 
2022 325&100 78.697 5.967 250&75 42.128 5.756 
2023 325&100 31.334 5.814 350&125 34.298 5.806 
2024 225&150 36.561 6.066 325&50 14.281 6.397 
2025 200&125 29.018 6.322 250&75 18.028 6.048 
2026 325&75 21.029 5.656 375&125 32.189 5.552 
2027 225&100 17.046 6.145 225&75 14.129 6.883 
2028 400&75 23.923 6.873 250&100 18.545 7.336 
2029 400&125 35.899 9.681 325&100 19.724 9.385 
2030 200&125 20.213 9.130 375&50 11.442 9.530 
2031 375&100 24.984 8.949 250&50 7.975 7.164 
Average 300&100 31.870 7.060 300&75 21.274 6.986 
A.C. Ozdemir et al. 
Resources Policy 78 (2022) 102906
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computationally efficient structure of the cell mechanisms of GRU net-
works which were discussed earlier. Thus, one of the original contri-
butions of this study is to unveil the outperforming characteristics of 
GRU networks against LSTM networks in terms of computational time. 
Moreover, Table 2 also reveals that the average number of hidden 
sizes and epochs for LSTM and GRU networks are determined as 
300&100 and 300&75 sequentially. These findings are crucial to give 
precious insights to prospective researchers in the field for not only 
narrowing the search limit in finding the optimal values along with 
providing a canonical standard for future studies, but also reducing the 
computational time for analyzes belonging to both LSTM and GRU 
networks. 
Fig. 6 shows the change in the historical and forecasted nickel price. 
It is understood that the nickel price has entered an upward trend since 
2007. In addition to this trend, the effect of the global financial crisis of 
2008 brought the nickel price to a historical peak of $52,179.1 per ton. 
Afterward, it is seen that there was descent at the same speed. However, 
the European debt crisis between 2009 and 2014 caused the nickel price 
to rise again. Although there were minor fluctuations after this crisis, it 
entered a relatively stable period. Finally, it is noticed that the recent 
COVID-19 pandemic has caused nickel prices to rise again. In the fore-
casted period, it is seen that the nickel price has taken on a more stable 
structure for both models. Also, nickel price is expected to vary between 
$10,000 and $20,000 per ton. 
5. Conclusions 
The main goal of this study is to forecast nickel prices in the medium- 
to long-term. Unlike other approaches in the literature, two advanced 
deep learning architectures were implemented, namely LSTM and GRU 
networks. The proposed models are tested on a data set consisting of 
monthly price data of eight metals (nickel, aluminum, copper, gold, 
iron, lead, silver, and zinc). The MAPE performance criterion was used 
to evaluate the obtained results. To conclude, the original findings of the 
study are as follows: 
1. The experiments on both networks showed that the networks are 
capable of yielding successful forecasting results. The average MAPE 
values for LSTM and GRU networks were calculated as 7.060% and 
6.986%, respectively. For both models, it is estimated that the nickel 
price might tend to vary between $10,000 and $20,000 per ton in the 
2022–2031 period, and it has been observed that the best forecast 
performance was obtained for the year 2026. 
2. In this study, it is found that GRU networks were 33% faster than 
LSTM networks, since the average computational time was calcu-
lated as 31.870 s for LSTM networks and 21.274 s for GRU networks. 
This is a significant observation because the future forecasts might be 
accomplished with bigger and high-resolution data which might be a 
bottleneck with current computing resources. 
3. The average number of hidden sizes and epochs for LSTM and GRU 
networks were determined as 300&100 and 300&75, respectively. 
These findings are valuable to prospective researchers in the field 
who will try to narrow the search limits of LSTM orGRU networks in 
finding optimal values and eventually provide a canonical standard. 
4. Keeping in mind that GRU networks are one step ahead with the 
advantage of computational time, it was expressed that both 
methods would overcome the price uncertainty problem of mine 
planning. This conclusion emphasizes that the proposed networks 
will be beneficial in making investment decisions, using resources 
efficiently, and increasing profitability. 
5. Finally, the recommendation of the study is to apply the proposed 
deep learning-based algorithms for forecasting the prices of other 
critical resources. 
Fig. 6. The historical and forecasted nickel prices. 
A.C. Ozdemir et al. 
Resources Policy 78 (2022) 102906
9
Credit authorship contribution statement 
Ali Can Ozdemir: Conceptualization, Investigation, Project admin-
istration, Resources, Writing - original draft, Writing - review & editing, 
Funding acquisition. Kurtuluş Buluş: Methodology, Resources, Soft-
ware, Validation, Formal Analysis, Visualization, Writing - original 
draft, Writing - review & editing. Kasım Zor: Data curation, Investiga-
tion, Methodology, Resources, Software, Supervision, Validation, Visu-
alization, Writing - original draft, Writing - review & editing, Funding 
acquisition. 
Funding sources 
This work was supported by the Scientific Project Unit of Çukurova 
University [grant number FBA-2019-11998] and by the Scientific Proj-
ect Unit of Adana Alparslan Türkeş Science and Technology University 
[grant number 21103013]. 
Declaration of competing interest 
None. 
Data availability 
Data will be made available on request. 
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https://doi.org/10.1109/3ICT53449.2021.9581373
	Medium- to long-term nickel price forecasting using LSTM and GRU networks
	1 Introduction
	2 Literature review
	3 Material and methods
	3.1 Material
	3.1.1 Data set information
	3.1.2 Descriptive statistics of data set
	3.2 Forecasting methods
	3.2.1 LSTM networks
	3.2.2 GRU networks
	4 Results and discussion
	5 Conclusions
	Credit authorship contribution statement
	Funding sources
	Declaration of competing interest
	Data availability
	References