=Paper=
{{Paper
|id=Vol-3105/paper18
|storemode=property
|title=Forecasting Gold Prices Using Temporal Convolutional Networks
|pdfUrl=https://ceur-ws.org/Vol-3105/paper18.pdf
|volume=Vol-3105
|authors=Justin Fajou,Andrew McCarren
|dblpUrl=https://dblp.org/rec/conf/aics/FajouM21
}}
==Forecasting Gold Prices Using Temporal Convolutional Networks==
https://ceur-ws.org/Vol-3105/paper18.pdf
Forecasting Gold Prices Using Temporal
Convolutional Networks
Justin Fajou1[0000−0003−0597−1941] and Andrew McCarren2[0000−0002−7297−0984]
1
Dublin City University, Dublin, Ireland justin.fajou2@mail.dcu.ie
2
Insight Centre for Data Analytics, Dublin City University
andrew.mccarren@dcu.ie
Abstract. Accurate prediction of the financial markets can provide
many benefits, of which underlying economic stability is probably the
most important. This area has understandably attracted a significant
amount of interest from the research community, and has inspired a di-
verse range of approaches with varying degrees of success. Gold is a
particular commodity which has attracted considerable attention since
it was first smelted for ornaments and jewellery by the Egyptians in
3600BC. In uncertain economic times it is regularly used as a safe-haven
commodity, and is why there is considerable attention given to enhancing
the accuracy of gold prices prediction methods.
Previous attempts at gold price prediction have used a variety of econo-
metric and machine learning techniques. In particular Long Short-Term
Networks (LSTMs) and more recently an ensemble of Convolutional Neu-
ral Networks (CNNs) and LSTMs have been found to have had consid-
erable level of success in time series prediction. In this research we have
conducted a comparative analysis between ARIMA, CNN, LSTM and
CNN-LSTM and a recently introduced structure known as Temporal
Convolutional Networks (TCNs) on gold price data spanning 20 years.
The results show how TCNs produced a RMSE of 15.26 and outper-
formed both CNN-LSTM and LSTM with RMSE scores of 23.53 and
27.39 respectively.
Keywords: TCN · Time Series · Commodities
1 Introduction
Gold was first traded as a futures contract on the Chicago Mercantile Exchange
(CME), following the collapse of the Bretton Woods agreement in 1971 [27].
This event decoupled the price of gold from money, which had required central
banks to purchase gold to support the value of their currencies. Subsequently,
the global economy gradually moved towards a US Dollar standard and away
from the gold standard. Nowadays, the US dollar is still regarded as the worlds
reserve currency and the benchmark price of gold is quoted in USD. In addition to
trading, the most common use for gold today is in the manufacture of jewellery,
which accounts for 80% of annual demand [6]. Due to its natural properties,
gold is also used in many industrial application such as mobile phones, computer
Copyright 2021 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0)
2 J Fajou and A McCarren
equipment and even in the production of specialist glazing to reduce heating and
ventilation costs in commercial buildings [6].
Throughout history, gold has always been seen as a source of value, especially
in times of uncertainty and is considered to be a secure asset to store wealth. Thus
gold is seen as a safe-haven investment and tends to rise when there is increased
uncertainty in the world economy and drops when economic activity increases [3].
Times of uncertainty have included war, recession or even the current Covid-19
pandemic, which has seen the price of gold rise significantly [38]. In addition, gold
has historically been used as a hedge against inflation, however according to [19]
the link is more apparent in bear markets so the correlation is not consistent
and dependent upon specific market scenarios.
The gold market is essential to a properly functioning economy, and because
of its influence and importance to the global economy, the prediction of gold has
received extensive attention by researchers, in order to understand the unique
factors that influence price changes. For example approaches ranging from tra-
ditional econometric models such as ARIMA (Auto-Regressive Integrated Mov-
ing Average) [13] and GARCH (Generalized Auto-Regressive Conditional Het-
eroskedasticity) [9] models, to machine learning approaches such as Support
Vector Machines (SVMs) [20] and Random Forests [25] have all been used to
predict gold in the past.
More recently, deep learning architectures have shown success when forecast-
ing time-series. Deep neural networks can be defined as having an input layer,
an output layer and multiple hidden layers that can extract granular features
from the input data. Artificial Neural Networks (ANNs) have been used to pre-
dict gold prices as in [30, 36]. Long Short-Term Networks (LSTMs), which are
a type of Recurrent Neural Network (RNN), have shown to be very effective at
sequence modelling [34]. They have also been used in conjunction with Convo-
lutional Neural Networks (CNNs) to predict gold prices as in [15, 26, 37].
1.1 Contribution
In this paper a comparative analysis between a number of univariate prediction
techniques and a relatively new deep learning approach known as Temporal
Convolutional Networks (TCNs) was undertaken to predict the price of gold.
This is the first examination of the predictive power of TCNs on gold prices [2].
This research will show that TCN models can be used as a viable alternative to
current state of the art deep learning models when predicting gold price.
1.2 Structure of Paper
The remainder of this paper is organised as follows: section 2 provides a literature
review of the current gold price prediction strategies and the current application
areas for TCNs; section 3 gives a detailed description of the data and methods
used in this study to forecast gold prices; section 4 gives an overview and com-
parison of the performance for all the models that were implemented; and finally
in section 5 we summarise our outcomes and outline potential future work.
Forecasting Gold Prices Using Temporal Convolutional Networks 3
2 Related Research
In this section we initially examine the use of machine learning in stock market
forecasting and then focus on the techniques used specifically in gold price pre-
diction. Finally, we explore the the latest research on TCNs, which provide the
basis for this paper.
2.1 Stock Prices
A ”Feature-Fusion LSTM-CNN” was used to predict stock prices in [22]. They
constructed a number of images, which were the fusion of the stock price and
volume images. These images were then fed to a CNN model, which incorpo-
rated residual connections to allow for a deeper network design [14]. A separate
time series of the stock and volume is then fed to a LSTM. The features were
then concatenated and inputted to fully connected layers. The predictions from
the LSTM-CNN outperformed both the individual CNN and LSTM models. In
this research the authors collected minute by minute data points from a S&P500
Exchange-Traded Fund (ETF), which generated nearly 100k data points. Evalu-
ation of their results was completed using the root mean squared error (RMSE),
the root mean absolute error (RMAE) and the mean absolute percentage error
(MAPE). Whilst they claim this approach produced very positive results, the
resulting model is quite complex and the data preparation required for the chart
generation would take a considerable amount of time.
A purely convolutional approach was used by Hoseinzade and Haratizadeh,
who presented a method they refer to as CNNPred [17]. They attempt to classify
the next days trading as ”Up” or ”Down” for the S&P500, NASDAQ, DJI, NYSE
and RUSSELL stock market indices. The first model, called 2D-CNNPred, used
two dimensional inputs that feed images to the CNN containing 60 days time
lags and 82 explanatory variables. The second approach known as 3D-CNNPred,
adds an additional dimension of features from the five financial indexes that are
being predicted. Both models use multiple convolution and pooling layers and
then flatten the data, which is fed to a fully-connected layer to produce the final
output. They used F-measure to evaluate their results with both models out-
performing the baselines, which included CNNs and ANNs. While they achieved
positive results using a convolutional approach and their architecture didn’t in-
clude LSTMs as part of their design.
2.2 Gold Prices
A whale optimization algorithm (WOA) was proposed to forecast gold prices
in [1]. The WOA is a meta-heuristic designed to optimize the search space, and
is used in conjunction with a multilayer perceptron neural network. There were
360 monthly gold prices used for the model, with an additional 10 predictor
variables such as commodity prices, currency prices and inflation. They used
mean absolute error (MAE) and RMSE to evaluate their findings. They found
85% increase in performance over baseline models which included ARIMA and
4 J Fajou and A McCarren
other meta-heuristic combinations with neural networks. It should be noted the
results are dependent on a small set of monthly gold prices.
Jianwei et al. [21] introduced a novel technique known as ICA-GRUNN (Inde-
pendent Component Analysis - Gated Recurrent Neural Network) to predict the
price of gold. Their method extracts features using ICA and passes these features
to a GRUNN to forecast gold prices. They used gold prices from Jan 1979 to
Dec 2017 to train and test the models. Evaluation of the models were performed
using mean absolute deviation (MAD), MAPE and RMSE. ICA-GRUNN model
outperformed the baseline models (ARIMA, LSTM and GRU (Gated Recurrent
Networks)), indicating this technique warrants further research.
The goal of Vidal and Kristjanpoller was to predict the volatility of gold [37].
They proposed using a CNN-LSTM hybrid model. One significant difference to
other studies is the use of a VGG16 network. VGG16 is a CNN that was pre-
trained on the ImageNet dataset [8]. In this study, it receives a time-series that
has been transformed to a RGB image. The LSTM model used log-transforms
of the price as input. Both feature spaces are concatenated and fed to a fully
connected layer to predict the volatility. They used gold spot prices from the
London Bullion Market Association (LBMA) from April 1968 to October 2017
and used MAE for their evaluation. Comparisons with baseline models showed
an 18% improvement on LSTM models.
Similarly, Liverieris et al. proposed a CNN-LSTM method for the prediction
of gold prices [26]. However, instead of concatenating the feature space, the model
was generated sequentially and fed to a fully connected layer. They used gold
prices from Jan 2014 to April 2018, sourced from https://finance.yahoo.com.
In addition to predicting the gold price, they also produced a classification of
whether the price would increase or decrease the next day. MAE and RMSE were
used for evaluation and they successfully beat the performance of their LSTM
base models for both gold price prediction and next day classification. However,
the classification results don’t appear to be much better than chance, with the
best accuracy score being 55.53%, but that could be related to the small dataset.
2.3 Temporal Convolutional Networks
The development of Temporal Convolutional Networks was significantly influ-
enced by the onset of WaveNet’s [31], which proposed the use of Dilated Causal
Convolutions within Residual Connections. TCNs were first used in the segmen-
tation and detection of video and were found to be successful compared to CNNs
and LSTMs on multiple datasets [24].
TCNs were first used on time series data by Bai et al. [2]. They proposed a
network with three key pillars: Causal Convolutions, Dilated Convolutions and
Residual Connections, and combined these three concepts, along with the more
typical neural network components of Dropout, Batch Normalization and the
Rectified Linear Units (ReLU) activation function to define the TCN network.
In this study a combination of accuracy, loss and perplexity were used to evaluate
the performance of the TCN on 11 sequencing tasks. The TCN outperformed
LSTM, GRU and RNN models in 10 out of 11 of those tasks.
Forecasting Gold Prices Using Temporal Convolutional Networks 5
As this concept is relatively new, there has not been an extensive volume
of research comparing the results of TCNs to LSTMs, when predicting stock
prices. [7] used trading data from 2017 for the top 100 stocks on the Shenzhen
Stock Exchange in 2017 which amounted to almost 10 million transactions. Using
recall, precision and accuracy to evaluate the classification of price changes, they
showed that TCNs outperformed both GARCH and LSTM baseline models.
2.4 Summary
To date, the most promising method used to predict gold prices has been the
CNN-LSTM hybrid model [26, 37]. However, TCN is a framework adapted from
CNNs for modelling sequential data [2] and has been found to have performed
well in comparison to LSTMs [2, 24].
3 Methodologies
This paper implements a TCN on gold prices to determine how it compares
to competing modelling approaches such as ARIMA, CNN, LSTM and a hybrid
CNN-LSTM. In this section we initially give a description of the data used in the
experimental analysis and following this briefly outline the methodology behind
the chosen machine learning networks.
3.1 Dataset
The dataset used for training and testing the models in this study was obtained
from Yahoo Finance via the yfinance library in the Python environment [11].
Specifically, the data was retrieved for Gold Futures using the symbol GC=F,
between the 30th August 2000 and 31st December 2020. The data was then
partitioned using a 80/20 split into training and test datasets. This meant the
training dataset contained 4055 data points from 30th August, 2000 to 2nd
December 2016 and the test set contained 1014 data points from 5th December
2016 to 31st December 2020. There was a further separation of the training set
with an 80/20 split for train/validation, with the validation set used to tune the
hyperparameters of all the models. To run the models effectively for a neural
network, the training set was transformed using z-score normalisation and the
time lag used was 64 days for each prediction.
3.2 Baseline Methods
ARIMA is a statistical model [4] that has been used extensively in time series
studies. ARIMA models use a combination of autoregression, differencing and
moving averages to forecast future values.
CNNs have been used extensively in image classification and have achieved
improved results over the State of the Art (SOA) in comparison to previous re-
search [23]. CNNs are able to achieve translational and scale invariance by learn-
ing from surrounding data points using convolutions and pooling techniques.
6 J Fajou and A McCarren
This concept has been applied to time series analysis as in [17, 40]. In addition,
regularisation techniques such as Dropout [35] and Batch Normalization [18]
have been developed to reduce over-fitting, resulting in better predictions when
applied to out-of-sample data.
LSTMs were first proposed in 1995 by Hochreiter and Schmidhuber, but were
not used extensively until machine learning began to gain traction. LSTMs are
a special type of Recurrent Neural Network (RNN). While RNNs have memory
that can be used to model sequence data they suffer from vanishing/exploding
gradient problem [16]. LSTMs avoid this issue by creating gates: Input, Output
and Forget. The Input gate decides which inputs should be allowed to propa-
gate through the model by using a sigmoid function. The Forget gate determines
which values should be dropped and finally the Output gate decides which values
should be moved to the next time step. LSTMs have now gained wide popularity
for sequential data modelling and have been used extensively for language mod-
elling [39], translation [28], speech recognition [12] and time series analysis [10].
Using a CNN to extract features and feeding them to a LSTM model has
proven to be a more powerful approach [26, 37]. The benefit of this hybrid ap-
proach, is to use the power of CNNs to extract features, which can then be fed
sequentially or in parallel to a LSTM, thus focusing on the temporal features of
the data elements.
3.3 Temporal Convolutional Networks
More recently, the concept of the Temporal Convolutional Network (TCN) was
introduced by Lea et al. [24]. Bai et al. built upon this concept for sequence mod-
elling [2], and is the approach used in this paper. They brought together three
key concepts that define a TCN: Causal Convolutions, Dilated Convolutions and
Residual Connections.
A causal convolution will only use current and prior data to produce its
output. This means that the prediction at time t is only dependent on data
elements up to time t as in Fig. 1. This shows the kernel can only see present
and past values and not any future values.
Causal convolutions are not sufficient, by themselves, to successfully process
long sequences. To achieve that, dilated convolutions are used to increase the
size of the receptive field. When the dilation factor is one, this is equivalent to a
regular convolution, however increasing the dilation factor to say two, will force
the filter to only perform calculations on every second element. This enables
the receptive field to be increased exponentially so the output is dependent
upon a much larger receptive field, which reflects a larger set of previous time
periods. TCNs use stacked convolutions with an increasing dilation factor, as
in Fig. 1. This ensures the filter can hit each historical data element being
processed, and also enables models to handle much longer historical data inputs.
The experiments in this paper used a kernel size of 3 with 64 filters.
Residual connections were introduced by He et al. [14] and produced state
of the art results on the ImageNet dataset [8]. Previously, deep networks archi-
tectures were confronted with vanishing/exploding gradients. However, residual
Forecasting Gold Prices Using Temporal Convolutional Networks 7
Fig. 1: Building blocks for a TCN:Dilated Causal Convolution
Fig. 2: Building blocks for a TCN:Residual Block
connections circumvent this issue by allowing the network to skip layers while
passing the identity matrix in accordance with the formula in (1), where H(x)
is the desired mapping, F(x) are the non-linear transformations and x is the
identity mapping.
H(x) = F(x) + x (1)
As the receptive field of a TCN is dependent on the depth of the network, it
becomes essential to create a deeper network in order to achieve a larger receptive
field. This paper implements residual connections, as in Fig. 2, using ”Residual
Blocks” with dilation factors of 1,2,4,8,16,32. The residual blocks use optional
1x1 convolutions which pass the input and are then added to the transformations
using element-wise addition. These residual blocks can then be stacked with
increasing dilation factors to achieve large receptive fields using a deep network.
8 J Fajou and A McCarren
To summarise, there are three main advantages of the TCN network [2].
Firstly, it allows data to be processed in parallel, as opposed to LSTMs which
require input to be unfolded and processed step-by-step. Secondly, in comparison
to LSTMs, TCNs provide a more stable gradient. Finally, the ability to control
the dilation factor, kernel size and layer depth provides a lot of control over the
receptive field, along with the ability for the output to be dependent on longer
data elements.
One of the potential disadvantages of a TCN is they need to input the entire
length of the history vector, which could be memory intensive, in contrast to
LSTMs which only store a fixed length hidden state.
4 Results
In this section a univariate comparative analysis between a number of TCN
architectures and four baseline approaches is given. Each approach attempted to
predict the next days price on a given univariate series of gold prices.The baseline
models selected were ARIMA, CNN, LSTM and the hybrid CNN-LSTM.
All models were implemented using the statsmodels library for ARIMA [33]
and the machine learning approaches were implemented using the keras [5] and
sci-kit learn libraries [32]. The metrics used to compare the success of the models
were the Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and
R-Squared. For the formulas in (2) and (3) the number of predictions is repre-
sented by N, with pi representing the predicted value and ai being the actual
value of the i-th instance. For the R-squared formula in (4), RSS represents the
sum of square of the residuals and TSS is the total sum of squares.
N
1 X
M AE = |pi − ai | (2)
N i=1
v
u
u1 X N
RM SE = t (pi − ai )2 (3)
N i=1
RSS
R2 = 1 − (4)
T SS
It’s clear from the results in Table 1 that the TCN approach significantly
outperformed all other baseline models with the TCN model producing a RMSE
of 15.26, MAE of 10.05 and R2 of 0.9954. The next best method was the hybrid
CNN-LSTM model producing a RMSE of 23.53, MAE of 15.40 and R2 of 0.9892,
demonstrating that the inclusion of the CNN as a feature extractor does reduce
the error over a stand-alone LSTM. However, it still falls short of the performance
of the TCN in this scenario. The LSTM, CNN and ARIMA models produced
RMSE scores of 27.39, 87.07 and 219.54 respectively.
The two best performing models, TCN and CNN-LSTM, were compared
using walk-forward cross validation. Five train/test datasets were built with each
Forecasting Gold Prices Using Temporal Convolutional Networks 9
Table 1: Model performance on Gold Price prediction against the test dataset
ARIMA CNN LSTM CNN-LSTM TCN
RMSE 219.54 87.07 27.39 23.53 15.26
MAE 147.69 76 19.5 15.4 10.05
2
R 0.0770 0.8534 0.9855 0.9892 0.9954
Table 2: Walk-Forward Cross Validation comparison between CNN-LSTM and
TCN models
TCN CNN-LSTM
Run RMSE MAE R2 RMSE MAE R2
1 123.66 107.65 -0.3959 140.88 106.26 -0.8118
2 71.69 49.66 0.8401 439.36 366.79 -5.004
3 198.67 181.36 -0.3017 148.45 118.43 0.2732
4 12.03 17.4 0.9702 12.5 9.51 0.9678
5 26.26 17.4 0.9872 29.08 18.77 0.9842
training set increasing in size for subsequent folds using the TimeSeriesSplit
library from sci-kit learn [32]. The results, shown in Table 2, provide further
evidence of the TCN model outperforming the CNN-LSTM.
A chart of the comparison between the ground truth and the predictions
from the TCN model, which was the best performing model, can be seen in Fig.
3. One thing to note is that all of the baseline models found it difficult to predict
the up-swing in prices towards the end of the series in 2020, which is likely where
most of the errors resulted. However, the TCN model was able to provide more
accurate predictions for this sector of the test dataset.
One further benefit, that became apparent when training the models, was the
CNN-LSTM model was much harder to optimize than the TCN. The amount of
time required to perform hyper-parameter tuning was extensive in comparison
to the TCN models. Also, the CNN-LSTM needed to run approximately 1000
epochs, but the TCN produced its best results in under 100 epochs. Both of
these points are important when considering both computational power and
time required to produce a model.
10 J Fajou and A McCarren
Fig. 3: Predictions versus Actual for the TCN model against the test dataset
5 Conclusion
This research undertook a comparative analysis between Temporal Convolu-
tional Networks (TCNs), the current state of the art machine learning approaches
and a traditional time series model in gold price prediction. The results demon-
strated that the TCNs consistently outperformed the other approaches chosen
in this study and reduced the error by more 27% in comparison with the best
preforming non-TCN approach.
While Gold has traditionally been the chosen safe-haven commodity, recent
market behaviour throughout the pandemic has indicated that crypto-currencies
have become potential alternates. While crypto-currency prediction has been ex-
tensively studied using deep learning approaches, understanding the relationship
with gold could potentially have an import impact on future predictions. While
this study focused on the performance of TCNs on univariate prediction and fu-
ture work would possibly benefit from the inclusion of exogenous variables such
as crypto-currencies,stock market indices and economic indicators [29].
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