Modeling and Trading the EUR/USD Exchange Rate Using Machine Learning Techniques

Abstract

The present paper aims in investigating the performance of state-of-the-art machine learning techniques in trading with the EUR/USD exchange rate at the ECB fixing. For this purpose, five supervised learning classification techniques (K-Nearest Neighbors algorithm, Naïve Bayesian Classifier, Artificial Neural Networks, Support Vector Machines and Random Forests) were applied in the problem of the one day ahead movement prediction of the EUR/USD exchange rate with only autoregressive terms as inputs. For comparison reasons, the performance of all machine learning techniques was benchmarked by two traditional techniques (Naïve Strategy and moving average convergence/divergence model). Trading strategies produced by the machine learning techniques of Support Vector Machines and Random Forests clearly outperformed all other strategies in terms of annualized return and sharp ratio. To the best of our knowledge, this is the first application of Random Forests in the problem of trading with the EUR/USD exchange rate providing extremely satisfactory results.

Full text

ETASR - Engineering, Technology & Applied Science Research
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269
www.etasr.com Theofilatos et al: Modeling and Trading the EUR/USD Exchange Rate Using Machine Learning Techniques
Modeling and Trading the EUR/USD Exchange Rate
Using Machine Learning Techniques
Konstantinos Theofilatos
Dpt of Computer Engineering and
Informatics
University of Patras
Patras, Greece
theofilk@ceid.upatras.gr
Spiros Likothanassis
Dpt of Computer Engineering and
Informatics
University of Patras
Patras, Greece
likothan@ceid.upatras.gr
Andreas Karathanasopoulos
London Metropolitan Business School
London,
United Kingdom
A.Karathanasopoulos@londonmet.ac.uk
Abstract— The present paper aims in investigating the
performance of state-of-the-art machine learning techniques in
trading with the EUR/USD exchange rate at the ECB fixing. For
this purpose, five supervised learning classification techniques
(K-Nearest Neighbors algorithm, Naïve Bayesian Classifier,
Artificial Neural Networks, Support Vector Machines and
Random Forests) were applied in the problem of the one day
ahead movement prediction of the EUR/USD exchange rate with
only autoregressive terms as inputs. For comparison reasons, the
performance of all machine learning techniques was
benchmarked by two traditional techniques (Naïve Strategy and
moving average convergence/divergence model). Trading
strategies produced by the machine learning techniques of
Support Vector Machines and Random Forests clearly
outperformed all other strategies in terms of annualized return
and sharp ratio. To the best of our knowledge, this is the first
application of Random Forests in the problem of trading with the
EUR/USD exchange rate providing extremely satisfactory results.
Keywords- EUR/USD Exchange Rate; future direction prediction;
Naïve strategy; MACD strategy; Naïve Bayesian Classifier; K-
Nearest neighbors classifier; SVM; Random Forests; leverage;
transaction costs
I. I
NTRODUCTION
The application of machine learning techniques for market
predictions has been widely established in the scientific
community. This paper deals with the application of a variety
of state-of-the-art machine learning techniques in the problem
of predicting the one day ahead movement direction of the
EURO-USD exchange rates. Developing high accuracy
techniques for predicting financial time series is a very crucial
problem for economists, investigators and analysts. The
traditional statistical methods, used by economists in the past
years, seem to fail to capture the discontinuities, the
nonlinearities and the high complexity of financial time series.
Complex machine learning techniques like Artificial Neural
Networks, Support Vector Machines (SVM) and Random
Forests provide enough learning capacity and are more likely to
capture the complex non-linear models which are dominant in
the financial markets.
Some approaches examining the performance of machine
learning techniques in trading with the EURO-USD exchange
rate have already been developed. In [1], Dunis and Williams
demonstrated the ability of Multi Layer Perceptron (MLP)
Artificial Neural Networks in modeling and trading with the
EUR/USD exchange rate. Their empirical results showed that
the MLP outperformed all other benchmark models used. Next,
in [2], Ullrich et al. used SVMs to trade with a variety of
foreign exchange rates including EUR/USD. Their results
indicated that SVMs outperformed Artificial Neural Networks
and all other traditional techniques used in this paper for
comparative reasons. Finally, in [3], Dunis et al. compared
Higher Order Neural Networks, Psi Sigma Networks,
Recurrent Networks and MLP in the task of trading with the
EURO/USD exchange rate. MLP was proved to outperform all
other neural networks variation.
The rest of the paper is organized as follows: In section II,
the dataset of EURO-USD exchange rates is presented. In
section III, all the traditional and machine learning techniques
used in the present paper are briefly described. In section IV
the comparative results are presented and in section V they are
discussed and some future research directions are proposed.
II. T
HE EUR
/
USD EXCHANGE RATES AND RELATED
FINANCIAL DATA
The European Central Bank (ECB) publishes a daily fixing
for selected EUR exchange rates: these reference mid-rates are
based on a daily concentration procedure between central banks
within and outside the European System of Central Banks,
which normally takes place at 2.15 p.m. ECB time. The
reference exchange rates are published both by electronic
market information providers and on the ECB’s website shortly
after the concentration procedure has been completed.
Although only a reference rate, many financial institutions are
ready to trade at the EUR fixing and it is therefore possible to
leave orders with a bank for business to be transacted at this
level.
The ECB daily fixing of the EUR/USD is therefore a
tradable level which makes using of a more realistic alternative
to, say, London closing prices and this is the series that we

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www.etasr.com Theofilatos et al: Modeling and Trading the EUR/USD Exchange Rate Using Machine Learning Techniques
investigate in the present paper. EUR/USD is quoted as the
number of USD per Euro.
Specifically, the data which are used for our problem were
downloaded from [4], and they were split as shown in Table 1
in order to train and evaluate our models.
TABLE I.
EURO
/
YSD DATASETS
.
Name of
period
Trading days Beginning End
Total dataset 2294 17 January 2002 30 December 2010
Training
dataset 1363 17 January 2002 16 May 2007
Validation
dataset 459 17 May 2007 2 March 2009
Testing dataset
[out of sample
dataset]
471 3 March 2009 30 December 2010
The graph in Figure 1 shows the total dataset for the
EUR/USD. As inputs to our models we selected a set of
autoregressive terms of the EUR/USD exchange rate returns
presented in Table 2.
Fig. 1. Euro/USD daily fixing prices (total dataset)
TABLE II.
EXPLANATORY VARIABLES
.
Number Input variable Lag
1 EUR/USD exchange rate return 1
2 EUR/USD exchange rate return 2
3 EUR/USD exchange rate return 3
4 EUR/USD exchange rate return 4
5 EUR/USD exchange rate return 5
6 EUR/USD exchange rate return 6
7 EUR/USD exchange rate return 7
8 EUR/USD exchange rate return 8
9 EUR/USD exchange rate return 9
10 EUR/USD exchange rate return 10
III. F
ORECASTING MODELS
A. Benchmark Models
In the present paper, the machine learning methods
presented in section 3.2 were benchmarked with 2 traditional
strategies, namely Naïve strategy [3] and a moving average
convergence/divergence technical model (MACD) [3].
The Naïve strategy takes the most recent period change as
the best prediction of the future change. The MACD strategy
used is quite simple. Two moving average series are created
with different moving average lengths. The decision rule for
taking positions in the market is straightforward. Positions are
taken if the moving averages intersect. If the short-term moving
average intersects the long term moving average from below a
‘long’ position is taken. Conversely, if the long-term moving
average is intersected from above a ‘short’ position is taken.
B. Machine Learning Models
Some of the state-of-the-art machines learning
classification techniques were applied in the problem of the one
day ahead prediction of the direction movement of the
EUR/USD exchange rate. These machine learning techniques
are: K-nearest neighbor classifier (KNN), Naïve Bayesian
classifier, Support Vector Machines (SVM) and Random
Forests. In order to find the optimal parameters for each
machine learning technique we used only the training and
validation datasets leaving the test set for the final evaluation of
the algorithms. Doing this we avoid specializing in our dataset
and getting misleading results. The parameters were optimized
using genetic algorithms [5]. All implementations were done
using Matlab R2009a edition.
K-nearest neighbors [6] is a method for classifying objects
based on closest training examples in the feature space. The
KNN method is considered one of the simplest machine
learning techniques. An object is classified by a majority vote
of its neighbors. If K=1, then the object is assigned to the class
of its nearest neighbor. In our case study the optimal K found
was 8.
The Naïve Bayesian classifier [7] is a simple probabilistic
classifier with strong assumptions of independence among
input variable. It is the classifier derived from the use of Bayes’
theorem. Bayes’ Theorem expresses the conditional
probability, or “posterior probability”, of a hypothesis H, (i.e.
its probability after evidence E is observed) in terms of the
“prior probability” of H, the prior probability of E and the
conditional probability of E given H. In implies that evidence
has a stronger confirming effect if it was more likely before
being observed. Bayes’ theorem is valid in all common
interpretations of probabilities, and it is commonly applied in
science and engineering. The main disadvantages of Naïve
Bayesian classifiers are their assumptions about the
independency of the input variables, which is not usually the
case in real problems.
Neural networks [8] exist in several forms in the literature.
The most popular architecture is the Multi-Layer Perceptron
(MLP). A MLP consists of at least three layers of nodes. The
network processes information as follows: the input nodes

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www.etasr.com Theofilatos et al: Modeling and Trading the EUR/USD Exchange Rate Using Machine Learning Techniques
contain the value of the explanatory variables. Each node of the
hidden layers passes incoming information through a nonlinear
activation function and passes it to the output layer if the
calculated value is above a threshold. Each node of one layer
has weighted connections to all other nodes of the next layer.
The training of the network (which is the adjustment of its
weights in the way that the network maps the input value of the
training data to the corresponding output value) starts with
randomly chosen weights and proceeds by applying a
supervised learning algorithm, called back propagation of
errors. Since networks with sufficient hidden nodes are able to
learn the training data (as well as their outliers and their noise)
by heart, it is crucial to stop the training procedure at the right
time to prevent overfitting (this is called ‘early stopping’). In
the present paper the best network’s architecture found was the
one using one hidden layer with 19 hidden neurons.
Support vector machines (SVM) are a group of supervised
learning methods that can be applied in classification and
regression problems. SVMs represent an extension to non
linear models of the generalized algorithm developed by
Vapnik [9]. They have already been applied in many scientific
problems. Specifically, SVM have already been used in many
prediction and classification problems in finance and
economics although they are still far from mainstream. The few
financial applications so far have only been published in
statistical learning and artificial intelligence journals. SVM
models were originally defined for the classification of linearly
separable classes of objects. For any original separable set of
two-class objects SVM are able to find the optimal hyperplanes
that separates them providing the bigger margin area between
the two hyperplanes. Furthermore they can also be used to
separate classes that cannot be separated with a linear classifier.
In such cases, the coordinates of the objects are mapped into a
feature space using nonlinear functions. The feature space in
which every object is projected is a high dimensional space in
which the two classes can be separated with the linear
classifier. In the present work we used the Radial Basis
Function (RBF) as Kernel function for the SVM models
because of its efficiency in providing very high performance
classification results. The optimal RBF parameters C and
gamma were found to be 64 and 2 respectively re-assuring that
the model does not over fit.
Another sophisticated machine learning method, such as the
support vector machines (SVM), is the random forest method.
Random forests [10] are ensemble classifiers that "grow" many
decision trees simultaneously where each node uses a random
subset of the features considered. Specifically, Random forests
are a combination of tree predictors such that each tree depends
on the values of a random vector sampled independently and
with the same distribution for all trees in the forest. The idea of
growing an ensemble of trees and letting them vote for the
most popular class has led to significant improvements in
classification accuracy. The generalization error for the forest
converges to a limit as the number of trees in the forest
becomes large. The generalization error for the forest of tree
classifiers depends on the strength of the individual trees in the
forest and the correlation between them. The optimal number
of classification trees found for our case study was 51 which
seem to be enough for achieving a very good generalization
performance. The applications of Random Forests in predicting
the movement direction of financial time series remains
nowadays quit limited despite of their high classification
performance and their ability to generalize in data that have not
been used to train their classifiers [11].
IV. E
MPIRICAL TRADING SIMULATION RESULTS
The trading performance of all models considered in the
validation subset is presented in Table 3. Due to the stochastic
nature of the machine learning techniques, every method was
executed 10 times and the results presented in Table 3 present
the mean performance of these executions. The trading strategy
derived for all the machine learning classification techniques
used in the present paper is simple and identical for all of them:
go or stay long if the classification model forecasts a positive
movement and go or stay short if the classification model
forecasts a negative movement. Since some of our models trade
quite often, taking transaction costs into account might change
the whole picture.
The transaction costs for a tradable amount, say USD 5-10
million, are about 1 pip (0.0001 EUR/USD) per trade (one
way) between market makers. But since we consider the
EUR/USD time series as a series of bid rates, we have to pay
the costs only one and not two times per position taken. With
an average rate of EUR/USD of 1.332 for the testing period, a
cost of 1 pip is equivalent to an average cost of 0.008% per
position.
TABLE III.
TRADING PERFORMANCE RESULTS
.
Naïve
Strategy
MACD KNN Naïve
Bayes
Information Ratio
(excluded costs) -0.48 0.27 -0.12 -0.21
Annualized Volatility
(excluded costs) 11.44% 11.46% 11.46% 11.46%
Annualized Return
(excluding costs) -5.51% 3.08% -1.36% -2.46%
Maximum Drawdown
(excluding costs) -26.54% -16.96% -13.98% -15.14%
Correct Directional
Prediction 49.24% 50.11% 48.83%
Transaction costs 1.04% 0.28% 0.90% 0.62
Annualized Return
(including costs) -6.59% 2.80% -2.26% -3.08
Artificial Neural
Networks (MLP)
SVM Random
Forests
Information Ratio
(excluded costs) 0.22 0.43 0.72
Annualized Volatility
(excluded costs) 11.46% 11.46% 11.45%
Annualized Return
(excluding costs) 2.51% 4.90% 8.29%
Maximum Drawdown
(excluding costs) -18.89% -14.74% -9.94%
Correct Directional
Prediction 50.12% 52.65% 53.50%
Transaction costs 0.92 0.92% 1.01%
Annualized Return
(including costs) 1.59% 3.98% 7.28

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As observed in Table 3, SVM and Random Forests
outperform all models in terms of annualized return and
information ratio even when transaction costs are considered.
Random Forests are the dominant model presenting the higher
minimum drawdown and thus reducing the trading risk.
Furthermore, as a classifier Random Forests demonstrated the
highest correct directional prediction in the out of sample
period and thus being the most accurate one.
V. C
ONCLUSIONS
In the present work, we applied a variety of machine
learning techniques in the problem of modeling and trading
with the EURO/USD exchange rate. From all the applied
machine learning techniques, Random Forests has not been
applied in this problem again while being one of the most
accurate classifiers. The machine learning techniques were
benchmarked with two traditional trading strategies: Naïve
strategy and MACD strategy.
Except from the simple methods of KNN and Naïve
Bayesian classifiers all other machine learning techniques
outperformed the traditional strategies that are even until now
used by economists. Thus, our empirical results encourage
future research in applying machine learning techniques in
trading with financial time series. From all the machine
learning techniques applied in the present paper, Random
Forests indicated the best trading performance in terms of
annualized return and information ration even when the
transaction costs were considered.
As a future direction we propose the application of random
forests and other machine learning techniques in trading with
other financial time series in order to test their performance and
establish them as reliable quantitative trading tools.
R
EFERENCES
[1] C. Dunis, M. Williams, “Modeling and trading the Euro/Us Dollar
exchange rate: do neural networks perform better?”, Derivatives Use,
Trading and Regulation, Vol. 8, No. 3, pp. 211-240, 2002.
[2] C. Ullrich, D. Seese, S. Chalup, “Foreign exchange trading with support
vector machines”, Advances in Data Analysis: Studies in Classification,
Data Analysis and Knowledge Organization, Part VII, pp. 539-546,
2007.
[3] C. Dunis, J. Laws, G. Sermpinis, “Modelling and trading the EUR/USD
exchange rate at the ECB fixing”, The European Journal of Finance,
Vol. 16, No. 6, pp. 641-561, 2010.
[4] Thomson Reuters Datastream: http://online.thomsonreuters.com/
datastream/ .
[5] J. Holland, Adaptation in natural and artificial systems: an introductory
analysis with applications to biology, control, and artificial intelligence,
Cambridge: Mass, MIT Press, 1995.
[6] T. Cover, P. Hart, “Nearest neighbor pattern classification”, IEEE Trans.
Inform. Theory, Vol. 13, No. 1, pp. 21-27, 1967.
[7] C. Howson, P. Urbach, Scientific Reasoning: The Bayesian Approach,
Third Edition, Open Course Publishing Company, 1993.
[8] S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice
Hall, 1998.
[9] V. Vapnik, The Nature of Statistical Learning Theory, Springer 2000.
[10] L. Breiman, “Random Forests”, Machine Learning, Vol. 45, No. 1, pp.
5-32 2001.
[11] K. Manish, M. Thenmozhi, “Forecasting stock index movement: A
comparison of support vector machines and random forest”. In
Proceedings of ninth Indian institute of capital markets conference,
Mumbai, India, 2005.
AUTHORS
PROFILE
Konstantinos Theofilatos is a PhD candidate in the Department of Computer
Engineering and Informatics of the University of Patras, Greece. In 2009, he
received a Master's degree from the Department of Computer Engineering and
Informatics of the University of Patras. His research interests include
computational and artificial intelligence, evolutionary computation, time
series modeling and forecasting, bioinformatics, data mining and web
technologies.
Spiros Likothanassis is an Electrical Engineer with a Ph.D. in Computer
Engineering and Informatics. He currently is a professor in the Department of
Computer Engineering and Informatics of the University of Patras. He is a
reviewer in many scientific journals and conferences including IEEE Neural
Networks, Journal of Knowledge and Information Systems, Information
Sciences Journal and Journal of Computational and Applied Mathematics. He
has a very good knowledge on Adaptive Signal Processing, Adaptive Control,
Computational and Artificial Intelligence, Intelligent Agents and
Bioinformatics. He has also experience in designing Information Systems, E-
commerce Applications, Distance Learning Systems and Teleworking
Applications
Andreas Karathanasopoulos is a senior Lecturer in London Metropolitan
Business School. In 2008 he received the Master of Science in International
Banking and Finance from the Department of Banking and Finance of
Liverpool John Moore’s University. His research interests include financial
forecasting, trading strategies, time series prediction, artificial and
computational intelligence and neural networks.