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Application of Machine Learning Algorithms for
Bitcoin Automated Trading
Kamil ˙
Zbikowski
Institute of Computer Science
Faculty of Electronics and Information Technology
Warsaw University of Technology
ul. Nowowiejska 15/19, 00-665 Warsaw, Poland
kamil.zbikowski@ii.pw.edu.pl
Abstract. The aim of this paper is to compare and analyze different
approaches to the problem of automated trading on the Bitcoin mar-
ket. We compare simple technical analysis method with more complex
machine learning models. Experimental results showed that the perfor-
mance of tested algorithms is promising and that Bitcoin market is still
in its youth, and further market opportunities can be found. To the best
of our knowledge, this is the first work that tries to investigate applying
machine learning methods for the purpose of creating trading strategies
on the Bitcoin market.
1 Introduction
Bitcoin is a peer-to-peer, decentralized electronic cash protocol. It is based on the
proof-of-work algorithm that uses cryptographic hash function for confirmation
of subsequent blocks of transactions. Block’s approval is realised by miners.
Skipping the details, the general idea behind is to find such a 32-bit field (called
nonce) that added to the block will result in a value of a hash function with
nleading zeros. Miners compete between each other to earn the incentive for
finding such a value. In order to achieve this goal, they have to employ the
computational power bearing the costs of hardware and electricity. The more
miners are engaged in the described process, the harder it is to find the required
value of hash function as more leading zeros are required in order to accept the
block. The measure describing this is called difficulty, and it is self-regulated by
the protocol.
Bitcoin was proposed by Satoshi Nakamoto in 2008 ([1]). Since then the whole
Bitocoin ecosystem has been growing rapidly. Since then it also raises questions
about some fundamental issues it promises. One of them is the anxiety about
the privacy and anonymity. More on this can be found in [2] and [3]. For a long
time, Bitcoin’s proof-of-work has been perceived as a safe to potential attacks.
Recently, there have been some concerns about that as well [4].
Despite some potential threats, Bitcoin community is growing and attracts
more and more attention both from the academia and business. In recent years,
2 Kamil ˙
Zbikowski
plenty of Bitcoin exchanges have been launched. The main advantage of them is
a simplification of trading and valuation of Bitcoin. As there is a market there
also exist investors, speculators and hedgers ready to exchange bitcoins and fiat
currencies. As it is done on traditional financial markets, one may be interested
in applying automated trading strategies that would help gain reasonable return
on invested funds. In this paper, we would like to test and compare several
approaches from traditional markets applied to the task of automated trading
on Bitcoin.
The remainder of this paper is organised as follows. Section 2 briefly describes
the concept of Support Vector Machines and Volume Weighted Support Vector
Machines. We also provide information about indicators used for the purpose of
presented experiments. In section 3 we provide information about data that was
used for computations. In 4 we analyze experiments’ results. Finally, in section
5 we make some concluding remarks.
2 Prediction Models
In order to investigate the existence of profitable automated trading algorithms,
we propose to use some of the most well-known approaches. First, we would like
to verify basic exponential moving average (EMA) with some simple enhance-
ments. Then, we would like to apply a much more sophisticated method that
directly employs machine learning methods like support vector machines (SVM)
in combination with box theory. Last but not least, we would like to deter-
mine whether some improvements in the machine learning algorithm, validated
against data from other financial markets, will also perform well.
2.1 Exponential Moving Average
First model that we use is exponential moving average (EMA) that is widely
known technical analysis indicator. It assigns to the more recent quotations,
higher weights basing on the assumption that they are more relevant than the
older ones. EMA for the moment tis defined recurrently as follows:
EM An
t= (Pt−EM At−1)α+EM At−1(1)
where Ptis the price for the moment t,αis defined as 2/(n+ 1) and the value
of EM A0is set to P0.
Signals to buy or sell are triggered when the EM At< Ptor EM At> Pt
respectively. Some traders believe that there exist predefined values of nthat
suit for every case. We took a rather different approach. We applied walk-forward
procedure ([5]) in order to re-optimise the model every 100 quotations. During
this step, we conduct an extensive search using grid search procedure looking
for the value of nfor the next moving window basing on last 200 quotations.
Application of Machine Learning Algorithms for Bitcoin Automated Trading 3
Table 1: Indicators used as the inputs of Box SVM and VW-SVM models (ndenotes
the data length used for computations; tis the index of the element in the time series).
Indicator Formula Box SVM VW-SVM
Close price Pt+ +
Volume Vt+ +
Average
Price µt=Pt
k=0 Pt−k
t- +
Standard
Deviation σt=qPt
k=0(Pt−k−µt)2)
t+ +
Relative
Strength
Index
RSI n
t= 100 −100
1+RSn
t
+ +
RSn
t=Pn
k=0 Uk
Pn
k=0 Dk
Ut=(Pt−Pt−1if Pt≥Pt−1
0 otherwise
Dt=(Pt−1−Ptif Pt< Pt−1
0 otherwise
Daily rate
of return Rt=Pt
Pt−1- +
%R
Oscillator
%Rn
t= 100 MaxP n
t−Pt
MaxP n
t
−MinP n
t
- +
M axP n
t= max{Pt, Pt−1,...,Pt−n}
M inP n
t= min{Pt, Pt−1,...,Pt−n}
Average
True
Range
AT Rn
t=1
nPn
i=0 T Rt−i- +
T Rt= max{PH
t−PL
t, P H
t−PC
t−1, P L
t−PC
t−1}
Vortex
Vn(+)
t=Pd
k=0(PH
t−k−PL
t−k)
Pd
k=0 T Rt−k- +
Vn(−)
t=Pd
k=0(PL
t−k−PH
t−k)
Pd
k=0 T Rt−k
On
Balance
Volume
OBVt=
OBVt−1+Vtif Pt> Pt−1
OBVt−1−Vtif Pt< Pt−1
OBVt−1if Pt=Pt−1
- +
2.2 Support Vector Machines with Box Theory
Support Vector Machine (SVM) is a machine learning algorithm that employs
the risk minimization principle that was described in [6]. Its general idea is based
on maximizing the margin of separating hyperplanes. This operation prevents
from building models that are overfitted and directly lowers the error obtained
4 Kamil ˙
Zbikowski
on the test sample. The general penalty function is defined as follows:
min
w∈H,b∈R
1
2||w||2+C
m
X
i=1
ξi,(2)
subject to:
yi(wxi−b)≥1−ξi,(3)
ξi≥0,(4)
where Cis a penalty term, ξiare slack variables, xiis the ith input value and
yiis the corresponding target value.
The model based on box theory and SVM was proposed in [7]. The box
theory assumes that in order to obtain valid buy or sell signals the price should
break through the oscillation box constructed over the specified period of time.
The input of the model consists of several technical indicators and statistical
measures gathered in Table 1.
2.3 Volume Weighted Support Vector Machines
The idea of Volume Weighted SVM was introduced in [5] and further investigated
in [8]. It is based on the simple, yet powerful, assumption that latest quotations
should have a greater impact while building a prediction model. To achieve this
goal, there was proposed a slight modification in a basic SVM formula 2 that
takes following form:
min
w∈H,b∈R
1
2||w||2+
m
X
i=1
Ciξi,(5)
In 5, each Citerm determines the weight assigned to particular input xiand
takes the form:
Ci=viC, (6)
where
vt=Pd
k=0 Vt−k
Pm
i=0 Wt−i
,(7)
where Vt−kis the real transactional volume for the moment t,kdepicts the delay
period and dis the data length required for feature calculation.
In [8], the formula 5 was used in combination with several technical indicators.
The list of indicators used as an input for VW-SVM for the purpose of the
experiment presented in this paper is enlisted in Table 1.
3 Research Data
For the purpose of presented experiment, we used data gather from one of the
largest Bitcoin exchanges in terms of average daily volume traded - Bitstamp
(www.bitstamp.com). It is available via their API. We have merged all the quo-
tations to the form of 15-minutes aggregates and as a price Ptwe have applied
Application of Machine Learning Algorithms for Bitcoin Automated Trading 5
the closing price of an aggregate from the moment t. The spectrum of selected
data consists of 2221 aggregates. It starts on January 9th 2015 and ends on
February 2th 2015.
Transactions’ costs vary depending on exchange and traded volume over time.
We assumed transaction fee at the level of 0.2% which seemed to be a reasonable
choice.
4 Empirical Study
We applied a walk forward testing[5] procedure that is a recommended method
for constructing machine learning models dedicated to time-series data. Each
algorithm was able to open both short and long positions. That is not directly
possible at the moment having an account open on the Bitstamp exchange. How-
ever, several competitors provide such a service for their customers. Therefore,
we got to the conclusion that this decision was justified.
Table 2: Backtesting results for EMA, Box SVM and VW-SVM models. Ris the rate
of return over the whole testing period, DD is the maximum drawdown experienced
by the algorithm.
R[%] DD[%]
EMA -59.11 64.30
Box SVM 10.58 25.94
VW-SVM 33.52 22.88
Buy & Hold 4.86 (28.10) 30.90
We run each of the models described in section 2 separately using data that
was collected according to section 3. The summary of these experiments is col-
lected in Table 2. We assume that initially, each of the algorithms holds a port-
folio of 100,000$.
In order to measure the degree of risk we provide a drawdown measure that is
computed as a maximum loss from the highest value of the equity that algorithm
was holding (expressed in percent). As an assessment of model’s performance,
we provide rate of return computed over the whole testing period. All results are
compared to the so-called buy and hold strategy that assumes opening a long
position at the beginning of available data and holding up to the end of data.
Each time the position is open by the algorithm it engages the whole capital
that it is holding at the particular moment. It is rather a weak position size
management. However, it is justified if we compare trading result to buy and
hold reference strategy.
Simple exponential moving average model lost 59.11%. As it can be seen
in the Figure 1 the equity line is declining throughout the whole tested period
6 Kamil ˙
Zbikowski
of time. The drawdown of this model reached 64.30%. This strategy obtained
the worst result in terms of both maximum drawdown and the rate of return.
The buy and hold strategy performed significantly better. From this outcome we
may conclude that even for such an immature market like it is in case of Bitcoin,
simple trading strategies based on technical analysis are not profitable.
Jan 15 Jan 20 Jan 25 Jan 30 Feb 04
50000 100000 150000
EMA
Equity
Fig. 1: EMA results. Black – buy & hold strategy, gray – EMA performance.
First of the advanced strategies that we were testing, namely Box SVM,
achieved much better results compared to EMA. Its rate of return was 10.58%
which is 5.72% improvement over buy and hold (see figure 2). In terms of the
maximum drawdown, it did not cross the level of 25.94% which still denotes a
high risk of investment. However, compared to buy and hold strategy, it achieved
4.96% improvement.
The second strategy that is based on SVM classifier, namely Volume-Weighted
SVM, managed to achieve the rate of return of 33.58%. Its equity curve is shown
in the figure 3. It is the highest return ratio among analyzed models. It is 28.66%
improvement over buy and hold strategy and 23% over Box SVM. Moreover,
VW-SVM exposure to the risk measured by the maximum drawdown was the
lowest. It was better than buy and hold by 8.02% and by 3.14% than Box SVM
model.
5 Conclusion
In this paper, we compare three different algorithms that are applied to the task
of trading on Bitcoin exchange. One of them was a simple technical indicator
based on the exponential moving average. Two others, namely Box SVM algo-
rithm and Volume-Weighted SVM, were selected from the literature. Both em-
Application of Machine Learning Algorithms for Bitcoin Automated Trading 7
Jan 20 Jan 25 Jan 30 Feb 04
80000 100000 120000 140000
SVMOscillationBox
Equity
Fig. 2: Box SVM results. Black – buy & hold strategy, gray – Box SVM performance.
Jan 20 Jan 25 Jan 30 Feb 04
80000 100000 120000 140000
VW−SVM
Equity
Fig. 3: VW-SVM results.0 Black – buy & hold strategy, gray – VW-SVM performance.
ploy SVM classifier and proved to be effective on other types of capital markets.
As it was shown in the empirical analysis, applying machine learning modelling
enhances the overall trading performance.
The obtained results are very promising. Assuming achieved scores, the com-
pound return over a one-year period would exceed reasonable levels known from
financial markets. It is a direct evidence that Bitcoin market is still young and
tends to be ineffective.
Future work will address the issue of position sizing and minimizing the
overall risk expressed in this paper by the mean of the maximum drawdown. It
8 Kamil ˙
Zbikowski
is also worth investigating other methods known from traditional markets. One
of them can be acquiring data from social networks and use it as an input for
machine learning algorithms in order to predict substantial price movements.
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