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Algorithmic Financial Trading with Deep Convolutional Neural

Networks: Time Series to Image Conversion Approach

Omer Berat Sezera,∗

, Ahmet Murat Ozbayoglua

aTOBB University of Economics and Technology, Ankara, 06560,Turkey

Abstract

Computational intelligence techniques for ﬁnancial trading systems have always been quite

popular. In the last decade, deep learning models start getting more attention, especially

within the image processing community. In this study, we propose a novel algorithmic trad-

ing model CNN-TA using a 2-D Convolutional Neural Network based on image processing

properties. In order to convert ﬁnancial time series into 2-D images, 15 diﬀerent technical

indicators each with diﬀerent parameter selections are utilized. Each indicator instance gen-

erates data for a 15 day period. As a result, 15x15 sized 2-D images are constructed. Each

image is then labelled as Buy, Sell or Hold depending on the hills and valleys of the original

time series. The results indicate that when compared with the Buy & Hold Strategy and

other common trading systems over a long out-of-sample period, the trained model provides

better results for stocks and ETFs.

Keywords: Algorithmic Trading, Deep Learning, Convolutional Neural Networks,

Financial Forecasting, Stock Market, Technical Analysis

1. Introduction

Stock market forecasting based on computational intelligence models have been part of

stock trading systems for the last few decades. At the same time, more ﬁnancial instruments,

such as ETFs, options, leveraged systems (like forex) have been introduced for individual

investors and traders. As a result, trading systems based on autonomous intelligent decision

making models are getting more attention in various diﬀerent ﬁnancial markets globally [1].

In recent years, deep learning based prediction/classiﬁcation models started emerging

as the best performance achievers in various applications, outperforming classical computa-

tional intelligence methods like SVM. However, image processing and vision based problems

dominate the type of applications that these deep learning models outperform the other

techniques [2].

∗I am corresponding author

Email addresses: oberatsezer@etu.edu.tr (Omer Berat Sezer), mozbayoglu@etu.edu.tr

(Ahmet Murat Ozbayoglu)

Preprint submitted to Applied Soft Computing April 28, 2018

In literature, deep learning methods have started appearing on ﬁnancial studies. There

are some implementations of deep learning techniques such as Recurrent neural network

(RNN) [3], convolutional neural network (CNN) [4], and long short term memory (LSTM)

[5]. In particular, the application of deep neural networks on ﬁnancial forecasting models

have been very limited.

CNNs have been by far, the most commonly adapted deep learning model [2]. Meanwhile,

majority of the CNN implementations in the literature were chosen for addressing computer

vision and image analysis challenges. With successful implementations of CNN models, the

model error rates keep dropping over years. Despite being one of the early proposed models,

AlexNet achieved 50-55% success rate. More recently, diﬀerent versions of Inception (v3,

v4) and ResNet (v50, v101, v152) algorithms achieved approximately 75-80% success rate

[2]. Nowadays, almost all computer vision researchers, one way or another, implement CNN

in image classiﬁcation problems.

In this study, we propose a novel approach that converts 1-D ﬁnancial time series into

a 2-D image-like data representation in order to be able to utilize the power of deep convo-

lutional neural network for an algorithmic trading system. In order to come up with such

a representation, 15 diﬀerent technical indicator instances with various parameter settings

each with a 15 day span are adapted to represent the values in each column. Likewise, x axis

consists of the time series of 15 days worth of data for each particular technical indicator

at each row. Also the rows are ordered in such a way that similar indicators are clustered

together to accomplish the locality requirements along the y-axis. As a result, 15x15 pixels

sized images are generated and fed into the deep convolutional neural network. To the best

of our knowledge, a 2-D representation of ﬁnancial technical analysis time series data and

feeding it as the input for a 2-D image classiﬁcation based deep CNN, namely CNN-TA,

for a ﬁnancial trading system is novel; since it has not been used not only for any trading

system, but also in any ﬁnancial prediction model the way we have proposed here. Perfor-

mance evaluation indicates, such an approach actually performs remarkably well even over

long periods. The proposed model outperformed Buy & Hold, common technical indicator

based models, most widely used neural network, namely MLP, and the state of the art deep

learning time series forecasting model, namely LSTM, on short and long out-of-sample pe-

riods. Even though, this is probably one of the ﬁrst attempts using such an unconventional

technique, we believe, the proposed model is promising. Moreover, parameter optimization

and model ﬁne tuning might even boost the performance even further.

The rest of the paper is structured as follows: After this brief introduction, the related

work is presented in Section 2 followed by the Model features described in Section 3. The

implementation methodology is given in Section 4 where the data, model and the algorithm

details are explained. Financial evaluation of the proposed model is analyzed in Section 5.

Finally we conclude in Section 6.

2

2. Related Work

2.1. Time Series Data Analytics

In literature, there are diﬀerent adapted methodologies for time series data analysis.

These can be listed as follows: statistical and mathematical analysis, signal processing,

extracting features, pattern recognition, and machine learning. Statistical and mathemat-

ical analysis in time series data can be achieved through determining the mathematical

parameters such as maximum, minimum, average, moving average, variance, covariance,

standard deviation, autocorrelation, crosscorrelation and convolution in the sliding window

[6]. Curve ﬁtting, regression analysis, autoregressive moving average (ARMA), autoregres-

sive integrated moving average (ARIMA), Bayesian analysis, Kalman ﬁlter methods are the

mathematical methods that are generally used to analyse and forecast time series data in

literature [7]. In addition, signal processing methods such as Fourier and wavelet trans-

forms are used to analyze the time series data. Discrete Fourier Transform (DFT), Discrete

Wavelet Transform (DWT), Piecewise Aggregate Approximation (PAA) are also used to

analyze time series data to extract features and ﬁnd the similarities within the data [8].

Unlike traditional approaches, machine learning models are also used in analyzing time se-

ries data and predictions. Machine learning algorithms that are mostly used in time series

data analytics are listed as follows: Clustering algorithms [9], hidden markov models [10],

support vector machines (SVM) [11],[12],[13], artiﬁcial neural networks (ANNs) [14], [15],

[16], [17] self organizing maps (SOM) [18],[19],[20].

Time-series forecasting is implemented in various ﬁelds such as wind speed forecasting,

stock price forecasting, electricity demand forecasting, pollen concentrations forecasting in

airborne, human activity recognition forecasting, user behaviour foracasting in internet of

things applications, and so on. In literature, there are many applications and usage of

machine learning on time series data analytics. Arizmendi [14] used ANN in the time series

data to predict pollens concentrations in the atmosphere and observed that predictions

using ANN performed better than traditional approaches. Srinivasan [15] used a four-layer

feedforward ANN to estimate the hourly electrical charge in the power system. Kaastra and

Boyd [16] developed an eight-step procedure involving an ANN model in predicting ﬁnancial

and economic time series data. Bezerianos [21] estimated and evaluated the pulse rate change

with radial-based function neural network (RBF). Li [22] used a back-propagation artiﬁcial

neural network (BPANN) and autoregressive (AR) models for estimating the highest values

of vibrations in high buildings, which are diﬃcult to measure with instruments. Guan [23]

analyzed the sensor data acquired by 40 motion sensors on human legs, by using ANN. With

this mechanism, human activities (running, walking, lying, jumping, etc.) are estimated with

97% accuracy. Choi [24] used ANN in the learning part of smart home system. Mohandes [13]

applied SVM and MLP on time varying wind speed data and compared the results. In the

ﬁeld of medicine, Morchen [19] used SOM for the extraction of patterns of muscle activities

and for the identiﬁcation of extracted patterns. An et al. [25] proposed a new electricity

demand forecasting model called ”MFES” that uses feed forward ANN. In their proposal,

after application of ﬁltering and seasonal adjustment process, ANN is used to predict future

demand. In ﬁnance, diﬀerent machine learning models are also used for forecasting future

3

values. Next subsection covers the ﬁnancial time series analytics methods in literature.

2.2. Financial Time Series Data Analytics

For stock market forecasting, traditional machine learning models have been quite pop-

ular. Some researchers directly implemented time-series forecasting based on the ﬁnancial

data, whereas others used technical and/or fundamental analysis data in order to achieve

good forecasting performance. ANN, genetic algorithms (GA), fuzzy rule-based systems, as

well as hybrid models are among the preferred choices.

Cavalcante et al. [1] surveyed all forecasting model approaches such as ANN, SVM,

hybrid mechanisms, optimization and ensemble methods in their survey. Besides, Krollner

et al. [26] reviewed machine learning based stock market forecasting papers in diﬀerent

categories such as ANN based models, evolutionary & optimization techniques, and mul-

tiple/hybrid methods. Most of the researchers used ANN models to forecast stock market

index values [27], [28]. Chen et al. [29] proposed a neural network model for forecasting and

trading the Taiwan Stock Index. Guresen et al. [30] evaluated the neural network models in

particular multi-layer perceptron (MLP) and dynamic ANN to predict NASDAQ stock in-

dex. In addition, Sezer et al. [31] proposed an ANN that uses the ﬁnancial technical analysis

indicators (MACD, RSI, Williams%R) to predict Dow30 stock prices turning points. Dhar

et al. [32] used a classical three layer MLP network in their studies to estimate the closing

values of the Indian Stock Exchange stocks. Researchers also studied various combinations

of network parameters (number of neurons in the input and hidden layers, learning rate) to

ﬁnd the best MLP conﬁguration. Vanstone et al. [33] used MLP to create a system that can

give buy/sell points for the Australian market. Fundamental analysis data (price earning

ratio, book value, return on equity (ROE) and dividend payout ratio) are used as inputs for

MLP.

In addition, genetic and evolutionary approaches are used to predict stock prices and

trends [34], [35]. Kwon [36] et al. proposed a RNN with GA optimization to forecast stock

values. They tested their proposals with 36 companies in NYSE and NASDAQ from 1992

to 2004. Sezer et al. [37] proposed a deep MLP approach with GA optimization to predict

Dow Jones 30 companies’ stock prices. In their studies, RSI parameters (buy value, buy

interval, sell value, sell interval) are determined with GA. Best points are used as training

data set in deep MLP. Evans et al. [38] used a GA to correct prediction errors and ﬁnd the

best network topology of MLP for forecasting foreign exchange (FOREX) data. Huang [39]

used GA to optimize the Support Vector Regression (SVR) parameters and to ﬁnd which

stock should be used as input for method. Pulido [40] used particle swarm optimization

(PSO) for the MLP network structure parameters (number of hidden layers and number of

neurons in layers and linkage) for time series prediction of the Mexican Stock Exchange.

Also, hybrid machine learning models are proposed to analyze ﬁnancial time series data.

Wang et al. [41] proposed a hybrid SVR model that is combined with principal component

analysis (PCA) and brain storm optimization (BSO) to forecast stock prices. In their pro-

posal, 20 diﬀerent technical indicators are chosen as input to their model. After processing

of PCA and BSO, SVR is applied on technical indicators. Mabu et al. [42] proposed the

use of an ensemble learning mechanism that combines MLP with a rule-based evolutionary

4

algorithm to be able to determine buy/sell points in stock prices. Ballings et al. [43] com-

pared the performances of ensemble solutions (random forest, adaboost and kernel factory)

with classiﬁer models (ANN, logistic regression, SVM and KNN) to estimate movements of

stocks in the market.

In ﬁnancial time series analytics, new approaches started appearing with increasing com-

putational intelligence capacity. In the following subsection, deep learning models used for

ﬁnancial time series analytics in literature will be mentioned.

2.3. Deep Learning

A neural network that utilizes Deep Learning is a speciﬁc type of ANN that consists

of multiple layers which have diﬀerent contributions at each layer in such a way that the

overall network performs better than its shallow counterparts [44]. There are diﬀerent types

of deep learning models namely Convolutional Neural Network (CNN), Recurrent Neural

Network (RNN), Deep Belief Networks (DBN), Restricted Boltzmann Machines (RBMs),

and Long Short Term Memory (LSTM) networks. Proposed deep learning models are used

for diﬀerent purposes. In literature, CNNs, DBN, RBM are mostly used for classiﬁcation and

recognition of the images. RNNs and LSTMs are used for analysis of the sequential data,

natural language processing, speech recognition and time-series data analytics. In addition,

CNNs are mostly used in image/video processing, classiﬁcation and recognition processes

[45], [46], [47], [48], but also used in natural language processing and sentence classiﬁcation

[49], [50].

Even though deep learning models, in particular deep CNNs have been among the most

popular choices in recent years, there are only a limited number of implementations of deep

neural networks for ﬁnancial problems. Ding et al. [51] proposed deep learning method for

event driven stock market prediction to extract news texts, information from internet and

newspapers. They also used a deep CNN and neural tensor network to model short-term

and long-term impacts of circumstances on stock price changes. They used S&P 500 stock

historical data to test their models. Langkvist et al. [52] surveyed the methods for analyzing

the time-series data in terms of RBM, autoencoder, RNN, deep learning, convolution and

pooling, and hidden markov model (HMM). In addition, they mentioned and surveyed the

deep learning methods to evaluate stock market indexes and prices in their review. Fischer

et al. [5] used LSTM to forecast the direction of trend for stocks of the S&P 500 between

1992-2015. Krauss et al. [3] compared deep neural nets, gradient-boosted-trees, random

forests in their research. They used deep neural network model to forecast stock prices in

S&P 500 between 1992 and 2015.

In addition, Yoshihara et al. [53] proposed an approach that uses RBM and DBN to

predict the trend of stock prices on the Nikkei Stock Exchange using news events. The

proposed solution was tested with ten Nikkei stocks and the results were compared with

SVM. Shen et al.[54] proposed a new model to forecast the exchange rates by combining

an advanced DBN and the conjugate gradient method. The proposed technique was com-

pared with feed forward neural networks. They concluded that the proposed deep learning

approach was better than the traditional methods. Tino et al. [55] compared the Markov

model (MM) and RNN methods with diﬀerent parameters to estimate the movements of the

5

German DAX and British FTSE indexes (volatiliy, etc.). According to the results obtained,

RNN could not give better results than MM. Deng et al. [56] proposed a method that uses

Deep direct reinforcement (DDR) method and fuzzy deep direct reinforcement (FDDDR)

method together with Recurrent DNN (RDNN). The proposed method was applied in the

Chinese futures market and commodity futures market (silver and sugar prices).

In their previous implementation [37], the authors used evolutionary algorithms to opti-

mize the technical analysis parameters of commonly used indicators and developed a deep

feedforward neural network using these optimized parameters as inputs. The results indicate

deep learning can achieve good learning and generalization of buy-sell points for individual

stocks over long out-of-sample test periods.

In literature, CNN is mostly used for image classiﬁcation / analysis problems, it is

generally not preferred for time series data analytics directly. Meanwhile, their success

in computer vision over traditional models is quite remarkable. For ﬁnancial time series

forecasting, deep learning algorithms, most commonly RNN and LSTM networks were the

preferred choices in recent years. At the same time, algorithmic trading systems mostly

depend on technical analysis indicators along with some other inputs. However, models

that integrate technical analysis data with deep neural networks is not very common in

literature. Moreover, using CNN with 2-D matrix representation of the technical analysis

data for algorithmic trading is novel. With the proposed study, technical analysis data

and deep CNN are combined. The diﬀerence between the proposed model and the other

methods is that the technical analysis data is applied on the prices to create feature vectors

and matrices (two-dimensional images); hence, the ﬁnancial time series forecasting problem

is implicitly converted into an image classiﬁcation problem. In this study, we aimed to

develop algorithmic trading models that can make ﬁnancial forecasts in the medium and

short term, with stable decisions that can provide maximum proﬁt and less risk (variance).

3. Model Features and Convolutional Neural Network (CNN)

For analyzing and developing inference models from ﬁnancial data, there are two widely-

adopted approaches: technical analysis and fundamental analysis [1]. Fundamental analysis

can be implemented through examining company speciﬁc ﬁnancial data such as balance

sheet, cash ﬂow, return on assets. Meanwhile, technical analysis can be implemented through

analyzing past ﬁnancial time series data using mathematical and/or rule-based modelling.

There are many technical indicators that are used for predicting future directions of ﬁnancial

assets. In our study, we used 15 separate technical indicators with diﬀerent time intervals.

Selected technical analysis indicators and their corresponding formulas are summarized in

Appendix.

CNN is a feedforward ANN that takes its inputs as 2-D matrices. Unlike a fully con-

nected neural network like MLP, the locality of data within the input vector (or matrix)

is important. Hence, the neighboring data points within the matrix should be carefully

chosen. This is not an issue for image classiﬁcation problems, since the aforementioned

requirement is satisﬁed directly because the neighboring pixels are related to each other in

both directions.

6

Figure 1: Generalized Convolutional Neural Network

CNN generally consists of two types of layers: the convolutional layer and the subsam-

pling layer. It structurally has successive convolutional and sampling layers. In convolution

layer, convolution operation is applied, results are passed to the next layer. In subsampling

layer, number of parameters and the spatial size of the representation are reduced. In the

last subsampling layer, the data becomes a one-dimensional vector. Finally, the last layer is

connected to a fully connected MLP. Through that, the high-level decision making is per-

formed just as in the case of a traditional classiﬁer. As a result, the previous layers of CNN

actually performs an implicit feature extraction. CNNs have a wide range of applications in

image and video recognition, natural language processing and expert systems. The general

CNN structure is shown in Figure 1 [57],[47].

4. Method

For our algorithmic trading model, we propose a novel method that uses CNN to deter-

mine the ”Buy” and ”Sell” points in stock prices using 15 diﬀerent technical indicators with

diﬀerent time intervals and parameter selections for each daily stock price time series to

create images. We also use Apache Spark, Keras and Tensorﬂow to create and analyze the

images and perform big data analytics. As can be seen in Figure 2, our proposed method

is divided into ﬁve main steps: dataset extract/transform, labelling data, image creation,

CNN analysis and ﬁnancial evaluation phases. Our objective is to determine the best ﬁt for

the buy, sell, and hold points in the time series of the associated stock prices.

4.1. Preprocessing (DataSet Extract/Transform)

In our study, the daily stock prices of Dow 30 stocks and daily Exchange-Traded Fund

(ETFs) prices are obtained from ﬁnance.yahoo.com for training and testing purposes. Stock

/ ETF prices between 1/1/2002 to 1/1/2017 are used for training and testing purposes.

We adapted a sliding window with retraining approach where we chose a 5 year period for

training and the following 1 year for testing, i.e. training period: 2002-2006, testing period:

2007. Then we moved both training and testing periods one year ahead, retrained the

model and tested with the following year, i.e. training period: 2003-2007, testing period:

7

Figure 2: Proposed Method for CNN-TA

2008. As a result, each year between 2007 and 2016 is tested using repeated retraining.

Figure 3 illustrates this sliding training and testing approach. In the ﬁrst step, dataset

extract/transform phase, the downloaded prices are normalized according to the adjusted

close prices.

4.2. Labelling

After extracting the data for the intended period in labelling phase, all daily close prices

are manually marked as “Hold”, “Buy”, or “Sell” by determining the top and bottom points

in a sliding window. Bottom points are labelled as “Buy”, top points are labelled as “Sell”,

and the remaining points are labelled as “Hold”. The structure of the labelling process is

given in Algorithm 1.

4.3. Image Creation

In image creation phase, for each day, RSI, Williams %R, WMA, EMA, SMA, HMA,

Triple EMA, CCI, CMO, MACD, PPO, ROC, CMFI, DMI, and PSI values for diﬀerent

intervals (6 to 20 days) are calculated using TA4J (Technical Analysis For Java)1library.

These particular indicators are mostly oscillator and trend based ﬁnancial time series ﬁlters

1https://github.com/mdeverdelhan/ta4j

8

Figure 3: Training and Testing Approach

that are commonly preferred by short to medium term traders. Since 6 to 20 days of

indicator ranges are used in our study, swing trades for 1 week to 1 month periods are

focused. Diﬀerent indicator choices and longer ranges can be chosen for models aiming for

less trades.

For each day a 15x15 image is generated by using 15 technical indicators and 15 diﬀerent

intervals of technical indicators. Meanwhile, each image uses the associated label ( “Hold”,

“Buy”, or “Sell”) with the sliding window logic provided in Algorithm 1. The order of the

indicators is important, since diﬀerent orderings will result in diﬀerent image formations.

To provide a consistent and meaningful image representation, we clustered indicator groups

(oscillator or trend) and similar behaving indicators together or in close proximity. Figure 4

illustrates sample 15x15 Pixel images that are created during the image creation phase.

In our study, there are approximately 1250 images for each stock price training data in

a 5 year period. Even though each year from 2007 to 2016 is tested separately, their results

are combined and corresponding annualized metrics are calculated to represent longer test

periods. Two sets of long term test periods are chosen to be able to verify the performance

of the proposed model in diﬀerent market conditions. Approximately 2500 images for each

stock price are generated for the ﬁrst test case (1/1/2007 to 1/1/2017) which is aimed to

verify the sustainability of the model performance in a 10 year span. In addition, 1250 test

images are used for the second test case (between 1/1/2007 to 1/1/2012) which covers the

2008-2009 ﬁnancial crisis period. For each stock and ETF, diﬀerent training and test data

image ﬁles are prepared and they are evaluated separately for their diﬀerent characteristic

features.

4.4. CNN

In our proposed CNN analysis phase, as can be seen in Figure 5, nine layers are used.

These are listed as follows: input layer (15x15), two convolutional layers (15x15x32, 15x15x64),

a max pooling (7x7x64), two dropout (0.25, 0.50), fully connected layers (128), and an out-

put layer (3). Dropout layers are added to prevent overﬁtting. In our proposed model

9

Algorithm 1 Labelling Method

1: procedure Labelling()

2: windowSize = 11 days

3: while(counter Row < numberO fD aysInF il e)

4: counterRow + +

5: If (counterRow > windowSize)

6: windowBeginI ndex =counterRow −windowSize

7: windowEndIndex =windowBeginIndex +windowSize −1

8: windowM iddleIndex = (windowBeginIndex +windowEndIndex)/2

9: for (i=windowBeginIndex;i <=windowEndIndex;i+ +)

10: number =closeP riceList.g et(i)

11: if(number < min)

12: min =number

13: minIndex =closeP riceList.indexO f(min)

14: if(number > max)

15: max =number

16: maxIndex =closeP riceList.indexO f(max)

17: if(maxIndex == windowMiddleI ndex)

18: result = ”SELL”

19: elif (minI ndex == windowM iddleIndex)

20: result = ”BUY ”

21: else

22: result = ”H OLD”

CNN-TA, 3x3 ﬁlter size is used for CNN ﬁlter. In literature, diﬀerent size of CNN ﬁlters are

adapted: 3x3, 5x5 and 7x7. Decreasing ﬁlter size generally results in catching more details of

the images. 3x3 is the smallest and most commonly used kernel size in the image processing

application (AlexNet [45]).Using a ﬁlter size of 3x3 provides the convolution capability with

closest neighbors’ (upper,lower,right,left,upper left,upper right,lower left,lower right) infor-

mation while processing the current layer; hence sharp variations within the image can be

captured. In our particular study, we also preferred 3x3 ﬁlter size, since we have relatively

small images (15x15) and there can be signiﬁcant intensity variations within the images (see

Figure 4 ).

In the proposed model CNN-TA, the adapted CNN structure is similar to the deep CNN

used in the MNIST algorithm except 28x28 images were used as inputs in that particular

implementation. LeNet CNN structures, [58] the deep CNN model with ﬁrst successful

results, consist of six layers. In addition, adding more layers increases the complexity of

the algorithm. Without a large training set, an increasingly complex network is likely to

overﬁt and reduce the accuracy on the test data. For future work, deeper models with more

processing layers can be conﬁgured when more training data is available.

In our proposed CNN structure, there are diﬀerent layers: convolutional, maxpooling,

dropout and full connected MLP layer. Convolutional layer consists of convolution operation.

10

Figure 4: 15x15 Pixel Labelled Sample Images After Image Creation Phase

Figure 5: CNN Process

Basic convolution operation is shown in Equation 1 (t denotes time). In addition, convolution

operation is implemented on two dimensional images. Equation 2 illustrates the convolution

operation of two dimensional image (I denotes input image, K denotes the kernel). Besides,

consecutive convolutional and maxpooling layers build the deep neural network structure.

Equation 3 provides the details about the neural network architecture (W denotes weights,

x denotes input and b denotes bias). At the end of the network, softmax function is used

to get the output. Equation 4 shows the softmax function (y denotes output) [59].

In this study, we implemented the CNN structure using Keras2, Tensorﬂow3infrastruc-

ture and each test run lasts for 200 epochs. Number of epochs is ﬁne-tuned with choosing

diﬀerent number of epochs in diﬀerent tests.

2https://keras.io/

3https://github.com/tensorﬂow

11

s(t) = (x∗w)(t) =

∞

X

a=−∞

x(a)w(t−a) (1)

S(i, j) = (I∗K)(i, j ) = X

mX

n

I(m, n)K(i−m, j −n).(2)

ei=X

j

Wi,jxj+bi.(3)

y=softmax(e) (4)

4.5. Financial Evaluation

In the last step, buy-sell decisions are made according to the predicted Buy, Sell, Hold

labels. With associated consecutive Buy-Sell pairs, ﬁnancial trades are implemented. These

trades are stored in a transaction table and each transaction is evaluated through a ﬁnancial

evaluation model. The results of the ﬁnancial evaluation will be presented in the next section

for the selected test periods.

Algorithm 2 summarizes the overview of the proposed algorithmic trading model.

5. Performance Evaluation

The overall performance of our proposed model CNN-TA is evaluated using two diﬀerent

evaluation criteria: Computational Model Performance and Financial Evaluation. Computa-

tional model performance evaluation presents the convolutional neural network performance,

i.e. how well the classiﬁer distinguishes between Buy, Hold and Sell classes. Financial eval-

uation shows the performance of the whole proposed model by implementing the real world

ﬁnancial scenario. Stocks are bought, sold or held according to the predicted label with the

actual stock prices.

5.1. Test Data

In the ﬁnancial evaluation phase, our proposed method (CNN-TA) is evaluated with

ETFs and Dow Jones 30 Stocks with diﬀerent time periods (2007-2012 for analyzing the

eﬀects of 2008 ﬁnancial crisis, 2007-2017 for evaluating the performance of the last 10 years).

Our proposed model is trained with ﬁve-years training data and tested with one-year out-

of-sample data. Then, the network is retrained with the next ﬁve-years training data (with

one year move ahead as explained in the previous section) and tested with next one-year

out-of-sample data. Selected ETFs and their descriptions are illustrated in Table 1. The

chosen ETFs have the highest trading volumes with enough training data.

12

Algorithm 2 Generalized Proposed Algorithm

1: procedure AllPhases()

2: Phase DataSet E/T:

3: dataset =read(open, close, high, low, adjustedClose, volume)

4: dataset.adjustRatio =dataset.close/dataset.adjustedClose

5: adjust(dataset.open, dataset.close, dataset.high, dataset.low)with adjustRatio

6: Phase Data Labelling:

7: calculate Label (Buy/Sell/Hold)using sliding window

8: Phase Image Creation:

9: calculate technical analysis values (RSI, EMA, M ACD..)f or each line in dataset

10: create 15x15 images

11: merge label and technical analysis values

12: normalize technical analysis values between [1,−1]

13: for(i= 0; i < 15; i+ +)

14: trainingDataset[i] = dataset.split(dates = (1997 + i)to (2002 + i))

15: testDataset[i] = dataset.split(dates = (2003 + i))

16: Phase CNN:

17: foreach(trainingDataset[i]and testDataset[i])

18: trainingDataset[i] = resample(trainingDataset)to solve data imbalance problem

19: model =CNN(epochs = 200, blocksize = 1028)

20: model.train(trainingDataset[i])

21: model.test(testDataset[i])

22: Phase Financial Evaluation:

23: foreach(trainingDataset[i]and testDataset[i])

24: evaluateResults()

Table 1: Selected ETFs and Their Descriptions

Name Description Inception Date Volume

XLF Financial Select Sector SPDR ETF 12/16/1998 71,886,065

XLU Utilities Select Sector SPDR ETF 12/16/1998 11,342,530

QQQ PowerShares QQQ ETF 10/03/1999 33,918,165

SPY SPDR S&P 500 ETF 1/22/1993 68,675,793

XLP Consumer Staples Select Sector SPDR ETF 12/16/1998 9,721,714

EWZ iShares MSCI Brazil Capped ETF 7/10/2000 19,613,073

EWH iShares MSCI Hong Kong ETF 3/12/1996 2,586,985

XLY Consumer Discret Sel Sect SPDR ETF 12/16/1998 4,257,841

XLE Energy Select Sector SPDR ETF 12/16/1998 16,494,257

5.2. Computational Model Performance

The prediction performance of the proposed model is analyzed. Even though, each

stock/ETF performance is considered separately, due to space constraints, only summary

results will be presented. Table 2 tabulates the confusion matrix for Dow-30 test data.

Table 3 illustrates the performance evaluation of the results obtained through the confusion

matrix for Dow-30 data. Recall values of class ”Buy” and class ”Sell” are better when

13

compared with class ”Hold”. However, classes ”Buy” and ”Sell” have worse precision values

compared to class ”Hold”. For stock trading systems, accurate entry and exit points (classes

”Buy” and ”Sell”) are important for the overall success of the trading algorithm. In our case,

most of the ”Buy and Sell” points are captured correctly by the proposed model. However,

a lot of false entry and exit points are also generated. This is mainly due to the fact that

”Buy” and ”Sell” points appear much less frequent than ”Hold” points, it is not easy for

the neural network to catch the ”seldom” entry and exit points without jeopardizing the

general distribution of the dominant ”Hold” values. In other words, in order to be able to

catch most of the ”Buy” and ”Sell” points (recall), the model has a trade-oﬀ by generating

false alarms for non-existent entry and exit points (precision). Besides, Hold points are not

as clear as ”Buy” and ”Sell” (hills and valleys). It is quite possible for the neural network

to confuse some of the ”Hold” points with ”Buy” and ”Sell” points, especially if they are

close to the top of the hill or bottom of the valley on sliding windows. Table 2 provides the

confusion matrix of Dow30 test data and Table 3 illustrates the evaluation of the confusion

matrix of Dow30 test data. Table 4 provides the confusion matrix of ETFs test data and

Table 5 illustrates the evaluation of the confusion matrix of ETFs test data. Performance

Evaluation results indicate that ETFs’ results (overall accuracy) are better than Dow30

results. This can be as a result of ETFs being more stable and less sensitive to events,

economic crises, political decisions compared to stocks making them less volatile. This lack

of volatility results in a more stable environment for algorithmic trading models to learn the

trading model easier.

Table 2: Confusion Matrix of Test Data (Dow-30)

Predicted

Hold Buy Sell

Actual

Hold 52364 18684 23592

Buy 1268 5175 3

Sell 1217 8 5059

Table 3: Evaluation Of Test Data (Dow-30)

Total Accuracy: 0.58

Hold Buy Sell

Recall 0.55 0.80 0.81

Precision 0.95 0.22 0.18

F1 Score 0.70 0.34 0.29

Table 4: Confusion Matrix of Test Data (ETFs)

Predicted

Hold Buy Sell

Actual

Hold 18629 5180 6498

Buy 478 1215 0

Sell 587 0 1127

14

Table 5: Evaluation Of Test Data (ETFs)

Total Accuracy: 0.62

Hold Buy Sell

Recall 0.61 0.72 0.66

Precision 0.95 0.19 0.15

F1 Score 0.75 0.30 0.24

5.3. Financial Evaluation

In the last step of our algorithmic trading model, the generated transactions are analyzed

using the ﬁnancial evaluation method. In our model, each stock is bought, sold or held

according to the predicted label. If the predicted label is “Buy”, the stock is bought at that

point with all of the current available capital (if not bought before already). If the predicted

label is “Sell”, the stock is sold at that price (if it has been bought). If the predicted label

is “Hold”, no action is taken at that point. During a ﬁnancial trade, if the same label

comes consecutively, only the ﬁrst label is activated and the corresponding transaction is

performed. Repeating labels are ignored until the label changes. Starting capital for ﬁnancial

evaluation is $10,000, trading commission is $1 per transaction. Financial evaluation scenario

is illustrated in Equation 5 (”S” denotes ﬁnancial evaluation scenario, ”tMoney” denotes

totalMoney, ”#OfStocks” denotes numberOfStocks). The corresponding formulas for the

evaluation metrics (presented in Tables 10 and 11) are listed in Equations 6, 7, 8, 9, 10, 11.

S=

#Of Stocks =tMoney

price ,if label=’Buy’

no action, if label=’Hold’

tMoney =price ∗#OfStocks if label=’Sell’

(5)

AR = (( totalM oney

startM oney )1

numberOf Y ears −1) ∗100 (6)

AnT =transactionCount

numberOf Y ears (7)

P oS =successT ransactionC ount

transactionCount ∗100 (8)

ApT =totalP ercentP r ofit

transactionCount ∗100 (9)

L=totalT ransactionLeng th

transactionCount ∗100 (10)

IdleR =data.length −totalT ransLeng th

data.length ∗100 (11)

15

5.4. Compared Models

Our proposed model is also compared with ”Buy&Hold” Strategy (BaH), RSI (14 days,

70-30), SMA (50 days), LSTM and MLP regression methods. Each method, model and

strategy has been implemented and relevant ﬁnancial calculation scenarios have been ana-

lyzed. In the ”Buy&Hold” strategy, the stock is bought at the beginning of the test data,

sold at the end of the test data. In the RSI model, the RSI value is calculated for each day

in the test data. If the RSI value of the corresponding test data is less than 30, buy signal

is generated. If the RSI value of the corresponding test data is more than 70, sell signal is

generated. In the SMA model, a 50-day SMA value is calculated for each day in the test

data. Buy signal is generated if the corresponding test data is more than 50 days-SMA

value, whereas if it is less than 50 days-SMA value, sell signal is generated. LSTM [5] and

MLP regression [30], [60] models are also used in the analysis of ﬁnancial time series data

in the literature. The implemented LSTM model is composed of 25 neurons (input layer: 1

neuron, hidden layer: 25 neurons, output layer: 1 neuron, dropout: 0.5, epoch: 1000, time

steps: 240) [5]. The implemented MLP is a model consisting of 4 layers (layers: 1,10,5,1,

dropout: 0.5, epoch: 200, time steps: 100) [5].

5.5. ETF Analysis

The average annualized return for our proposed method (ETFs-2007-2017) is 13.01%

and percent of successful transactions is 71.51% (Table 11), whereas BaH average annual-

ized return is 4.63%, RSI model average annualized return is 3.95%, SMA model average

annualized return is 2.81%, LSTM model average annualized return is 6.22%, and MLP

regression average annualized return is 4.01% (Table 6). Proposed method’s average annu-

alized return is almost three times better than BaH, RSI, SMA, MLP regression average

annualized returns. At the same time, our proposed model and MLP regression are the

only models with positive annualized returns for all ETFs during the 10 year test period.

Meanwhile, the standart deviation of annualized returns of our model is also low indicating

stable and consistent returns. (Table 6). Figure 6 shows the proposed model’s accumulation

of the capital for selected ETFs. In each case, the model performance is compared against

Buy&Hold during the corresponding period. The performance results for other ETFs also

show similar characteristics.

The method is also tested and compared against other aforementioned models for the

test period between 2007-2012 which coincides with the 2008-2009 ﬁnancial crisis. The stock

market was hit very hard during that period and a lot of stocks/funds/ETFs had negative

returns. During that period, the average annualized return for our proposed method (ETFs-

2007-2012) is 13.17% and percent of successful transactions is 71.44% (Table 11), whereas

BaH average annualized return is 2.60%, RSI model average annualized return is -0.01%,

and SMA model average annualized return is 1.30%, LSTM model average annualized return

is 8.44%, and MLP regression average annualized return is 8.23%, (Table 7). Proposed

method’s average annualized return is almost ﬁve times better than BaH average annualized

return in that particular period. In addition, our proposed solution’s average annualized

return is almost 1.5 times better than LSTM and MLP regression average annualized returns

during the ﬁnancial crisis period. The standart deviation for the annualized returns was

16

Figure 6: Comparison of the Proposed Algorithm and BaH Method Results on XLE and XLF ETFs

Table 6: Comparison of Annualized returns of the Proposed System (CNN-TA) with BaH, RSI, SMA,

LSTM, MLP Reg. Models (ETFs - Test Period: 2007 - 2017)

ETFs CNN-TAr BaHr RSIr SMAr LSTMr[5] MLPr[5]

SPY 10.77% 4.63% 6.14% 0.54% 3.35% 7.27%

QQQ 11.57% 10.52% 6.46% 5.37% -1.33% 3.92%

XLU 10.13% 2.97% 4.91% 0.90% 1.29% 1.12%

XLE 15.80% 2.85% 3.64% 5.88% 4.01% 5.41%

XLP 11.10% 6.92% 5.29% 5.17% 5.97% 0.84%

XLY 9.55% 7.68% 5.74% 1.80% 2.13% 1.31%

EWZ 20.40% -3.38% -3.25% 4.15% -1.30% 5.42%

EWH 11.69% 1.73% 2.32% 3.08% 12.30% 6.11%

XLF 16.05% 2.31% 1.22% -5.60% 16.18% 2.68%

Average 13.01% 4.63% 3.95% 2.81% 6.22% 4.01%

St.Dev. 3.61% 4.03% 3.12% 3.57% 5.96% 2.40%

higher for this period when compared with 2007-2017 case. However, when compared with

the other models, it was still better than the majority. (Table 7).

Table 7: Comparison of Annualized returns of the Proposed System (CNN-TA) with BaH, RSI, SMA,

LSTM, MLP Reg. Models (ETFs Test Period: 2007 - 2012)

ETFs CNN-TAr BaHr RSIr SMAr LSTMr[5] MLPr[5]

SPY 9.25% -0.39% -1.64% -1.56% 11.05% 10.62%

QQQ 8.75% 5.73% 2.60% 6.35% 5.38% 2.85%

XLU 12.43% 3.72% 0.84% 0.13% 6.89% 3.78%

XLE 23.41% 5.61% -0.32% 7.45% 3.76% 12.93%

XLP 12.59% 6.97% 3.88% 4.07% 1.20% 4.37%

XLY 5.43% 1.65% 2.00% -3.68% 3.88% 7.41%

EWZ 25.07% 7.64% -1.54% 7.55% 1.69% 3.54%

EWH 12.32% 1.75% -0.01% -0.63% 26.07% 17.64%

XLF 9.34% -16.91% -7.68% -16.06% 6.39% 7.02%

Average 13.17% 2.60% -0.01% 1.30% 8.44% 8.23%

St.Dev. 6.69% 7.49% 3.36% 7.44% 7.61% 5.03%

5.6. Dow30 Analysis

As mentioned earlier, our proposed method was also evaluated with Dow Jones 30 Stocks

in diﬀerent time periods (2007-2012 and 2007-2017). Our proposed method’s (Dow30-2007-

17

2017) average annualized return is 12.59% and percent of successful transactions is 71.32%

(Table 10), whereas BaH average annualized return is 10.47%, RSI model average annual-

ized return is 5.01%, SMA model average annualized return is 3.78%, LSTM model average

annualized return is 6.48%, and MLP regression average annualized return is 5.45%. The

analyses provided for ETFs are also applicable to Dow30 performance, since similar out-

comes are observed. The proposed model performed the best overall annualized return with

a relatively low standart deviation. (Table 8). Figure 7 shows the proposed model’s accu-

mulation of the capital for diﬀerent Dow30 stocks. In each case, the model performance is

compared against Buy&Hold during the selected period. The performance results for other

Dow30 stocks also show similar characteristics.

Figure 7: Comparison of the Proposed Algorithm and BaH Method Results on JPM and TRV stocks

In addition, during the ﬁnancial crisis period the average annualized return for our

proposed method (Dow30-2007-2012) is 12.83% and percent of successful transactions is

70.63% (Table 10), whereas BaH average annualized return is 6.98%, RSI model average

annualized return is 1.92%, and SMA model average annualized return is 0.75%, LSTM

model average annualized return is 10.82%, and MLP regression average annualized return

is 9.98%. In addition, our proposed solution’s average annualized return is almost twice as

BaH annualized return during ﬁnancial crisis period. Again, the proposed model achieved the

best overall performance while keeping the variance low. These results show that proposed

solution is more stable than the other models (Table 9).

5.7. Discussions

Consistenly beating Buy and Hold strategy is challenging in a long period of time (like

10 years). Our proposed method’s (Dow30-2007-2012) annualized return performed better

than BaH strategy’s annualized return in 24 out of 28 stocks during the out-of-sample test

period (Table 9) (In the same period, Visa stock [V] did not have suﬃcient data points, so V

is neglected. Also Dupont [DD] stock prices had data inconsistencies in ﬁnance.yahoo.com,

so that was not used in the analyses.). In addition, our proposed method’s (ETF-2007-

2012) annualized return performed better than BaH strategy’s annualized return in 9 out of

9 ETFs during the out-of-sample test period (Table 7).

18

Table 8: Comparison of Annualized returns of the Proposed System (CNN-TA) with BaH, RSI, SMA,

LSTM, MLP Reg. Models (DOW30 - Test Period: 2007 - 2017)

Stock CNN-TAr BaHr RSIr SMAr LSTMr[5] MLPr[5]

MMM 10.88% 11.36% 4.64% 2.25% 6.43% 2.28%

AXP 25.05% 4.25% -0.85% -0.96% 7.23% 9.56%

APPL 11.37% 26.42% 10.11% 19.55% 5.03% 2.57%

BA 7.03% 8.60% 2.30% 2.07% 4.01% 2.59%

CAT 4.33% 7.19% -3.02% 10.72% -1.53% 0.66%

CVX 14.91% 8.67% 4.60% 1.07% 7.63% 5.76%

CSCO 10.02% 2.76% 5.57% -5.28% 9.05% 9.15%

KO 11.13% 8.85% 7.78% 3.09% 3.70% 2.71%

DIS 13.97% 13.14% 0.96% 6.36% 4.67% 5.36%

XOM 14.51% 4.78% 4.81% -2.34% 6.67% 3.46%

GE 10.35% 2.17% -7.35% 3.92% 4.74% 5.74%

GS 6.18% 2.35% -4.92% 2.83% 5.24% 11.62%

HD 15.20% 15.91% 7.07% 5.34% 6.27% 2.12%

IBM 8.15% 7.77% 5.35% 2.37% 0.91% -1.52%

INTC 18.23% 8.99% 5.18% 5.90% 6.18% 4.71%

JNJ 13.45% 9.01% 7.53% 1.81% 3.76% 0.42%

JPM 12.79% 8.25% 8.66% -4.77% 15.72% 16.27%

MCD 17.94% 14.43% 8.37% 2.04% 4.09% 0.24%

MRK 15.93% 6.55% 3.60% 0.91% 2.88% 5.46%

MSFT 13.43% 9.95% 7.07% 5.58% 5.29% 4.45%

NKE 18.00% 17.10% 9.34% 0.58% 1.54% 4.68%

PFE 8.07% 6.51% -0.35% 1.83% 7.07% 1.34%

PG 9.79% 5.72% 3.31% 0.88% 4.99% 3.93%

TRV 17.34% 12.01% 6.24% -7.62% 19.98% 10.97%

UTX 9.36% 7.67% 2.76% 3.18% 6.52% 1.65%

UNH 9.74% 13.21% 7.31% 9.50% -1.01% 2.13%

VZ 10.23% 9.29% 9.37% 0.28% 4.49% 5.63%

WMT 15.20% 6.28% 5.22% -2.88% 5.30% 8.33%

Average 12.59% 10.47% 5.01% 3.78% 6.48% 5.45%

St.Dev. 4.45% 5.10% 4.38% 5.28% 4.26% 3.99%

When Table 10 and Table 11 are analyzed, it is observed that Percent of Success for Trade

Transactions are between 70-80%. Hence, the trades generated by the proposed model are

successful (proﬁtable) most of the time. Since the out-of-sample test period is selected as 10

years, diﬀerent market conditions are observed during such a lengthy period (i.e. uptrend,

downtrend, stationary). But these ﬂuctuations in the market conditions did not aﬀect the

overall trading performance of the proposed model. As a result, the model was able to

generate good proﬁts even under deteriorating market conditions. For the most commonly

traded ETFs, the proposed model (ETF-2007-2017) outperformed the Buy & Hold strategy

9 out of 9 times (Table 6) and for Dow30 stocks, the proposed model (Dow30-2007-2017)

outperformed Buy & Hold 22 out of 28 times over the span of 10 years (Table 8).

5.8. Statistical Signiﬁcance Tests

The statistical signiﬁcance test results tabulated in Table 10 and Table 11 indicate the

proposed model does not change its behavior neither for diﬀerent asset classes (Dow30

stocks or ETFs) nor between diﬀerent time periods and varying market conditions (2007-

2012 and 2007-2017 time periods). For most of the evaluation metrics, the proposed model

shows stable and robust operating characteristics. Even though statistically no signiﬁcant

19

Table 9: Comparison of Annualized returns of the Proposed System (CNN-TA) with BaH, RSI, SMA,LSTM,

MLP Reg. Models (DOW30 - Test Period: 2007 - 2012)

Stock CNN-TAr BaHr RSIr SMAr LSTMr[5] MLPr[5]

MMM 13.42% 3.52% -1.58% -6.63% 15.26% 3.24%

AXP 31.64% -2.21% -11.33% -5.65% 27.47% 24.68%

APPL 10.03% 36.54% 7.54% 32.73% 20.92% 0.49%

BA 2.73% -0.56% 0.30% 1.82% 13.53% 3.94%

CAT 0.22% 10.97% -8.82% 17.61% 4.75% 4.56%

CVX 19.77% 11.87% 2.49% -0.02% 16.31% 14.09%

CSCO 8.34% -7.05% 0.13% -15.38% 0.80% 20.82%

KO 14.15% 11.13% 4.67% 5.13% 5.83% 8.25%

DIS 13.33% 3.55% -1.92% -4.28% 8.47% 3.11%

XOM 18.92% 5.12% 4.45% -5.17% 3.66% 9.15%

GE 7.11% -9.62% -17.51% -3.02% 3.73% 3.20%

GS 1.47% -15.00% -13.65% -4.50% -11.25% 6.41%

HD 12.01% 4.32% 2.77% -7.59% 5.23% 6.21%

IBM 11.61% 15.52% 4.46% 6.55% 1.34% -1.14%

INTC 18.56% 6.42% 4.08% 0.68% 7.82% 15.83%

JNJ 16.63% 3.03% 4.81% -3.09% 7.52% 2.63%

JPM 9.19% -5.84% 5.93% -19.40% 33.74% 29.12%

MCD 21.86% 22.14% 9.49% 0.91% -2.18% 2.45%

MRK 13.15% 0.33% -3.89% -1.21% 6.95% 11.71%

MSFT 4.44% -1.24% -2.50% 0.62% 12.58% 16.02%

NKE 19.12% 16.93% 12.80% -6.01% 11.80% 6.30%

PFE 8.56% 0.99% -5.84% -0.82% 2.92% 7.97%

PG 10.47% 3.26% 2.53% -2.33% 12.92% 1.12%

TRV 23.01% 5.91% 5.77% -18.90% 21.79% 15.03%

UTX 10.65% 4.37% 3.53% 2.39% 5.41% 3.40%

UNH 2.38% 0.22% -1.85% 7.59% -8.37% -0.09%

VZ 14.56% 7.95% 9.59% -3.16% 13.46% 16.30%

WMT 21.82% 6.89% 10.37% -10.88% 12.91% 13.09%

Average 12.83% 6.98% 1.92% 0.75% 10.82% 9.98%

St.Dev. 7.38% 10.09% 7.33% 10.21% 9.74% 7.77%

diﬀerences are observed for the proposed model’s trading performance under diﬀerent market

conditions, the proposed model performs better than traditional trading models like Buy &

Hold, RSI, SMA, LSTM and MLP regression especially when the overall market is not in

an uptrend.

Also, in Table 10 and Table 11 some trading summary results are provided. The results

are consistent not only between ETFs and Dow30 stocks, but also between varying market

conditions (2007-2012) and (2007-2017) periods. The number of transactions (AnT) are

between 17 and 21 in all cases indicating the model performs a trade (buy-sell pair) once

every 3 weeks which is consistent with the input technical analysis resolution (6 to 20 days).

Average trade length (L) is also 7 to 9 days which indicates there is also 9-14 days of idle

time where the model sits on cash waiting for a trade trigger (indicated by Idle Ratio).

In addition, the statistical signiﬁcance test results of proposed CNN-TA compared with

BaH, LSTM and MLP are tabulated in Table 12 and Table 13. The results indicate CNN-TA

trading performance is signiﬁcantly better than all models over the long run (2007-2017) for

both Dow30 stocks and ETFs. For 2007-2012 period, the outcome is similar, however only

for the LSTM case, the outperformance of CNN-TA is not signiﬁcant.

20

Table 10: TTest Results and Average Results of the Proposed CNN-TA Model for Dow30

Performance Metrics TTest Avg(07-12) Avg(07-17)

Proposed CNN Strategy

Annualized Return (CNN-TAr) 0.337 12.83% 12.59%

Annualized Number

of Transaction (AnT) 0.007 19.1 21.3

Percent of Success (PoS) 0.556 70.63% 71.32%

Average Percent Proﬁt

Per Transactions (ApT) 0.981 0.78% 0.78%

Average Transaction

Length in Days (L) 0.000 9.0 6.9

Maximum Proﬁt Percentage

in Transaction (MpT) 0.127 11.04% 8.82%

Maximum Loss Percentage

in Transaction (MlT) 0.052 -18.97% -14.33%

Idle Ratio (IdleR) 0.002 53.32% 57.11%

Sharpe Ratio (Daily) - 0.08 0.10

Table 11: TTest Results and Average Results of the Proposed CNN-TA Model for ETFs

Performance Metrics TTest Avg(07-12) Avg(07-17)

Proposed CNN Strategy

Annualized Return (CNN-TAr) 0.787 13.17% 13.01%

Annualized Number

of Transaction (AnT) 0.298 18.8 17.3

Percent of Success (PoS) 0.982 71.44% 71.51%

Average Percent Proﬁt

Per Transactions (ApT) 0.815 0.74% 0.70%

Average Transaction

Length in Days (L) 0.405 8.8 9.4

Maximum Proﬁt Percentage

in Transaction (MpT) 0.962 9.98% 10.12%

Maximum Loss Percentage

in Transaction (MlT) 0.747 -19.84% -18.51%

Idle Ratio (IdleR) 0.546 52.64% 54.04%

Sharpe Ratio (Daily) - 0.09 0.11

Table 12: TTest Results of Annualized Return of Dow30 Stocks

Time Interval Performance Metrics TTest Results

2007-2017

CNN-TA - BaH 0.0100241

CNN-TA - LSTM 0.0000001

CNN-TA - MLP 0.0000001

2007-2012

CNN-TA - BaH 0.0012111

CNN-TA - LSTM 0.1072803

CNN-TA - MLP 0.0490155

Table 13: TTest Results of Annualized Return of ETFs

Time Interval Performance Metrics TTest Results

2007-2017

CNN-TA - BaH 0.0000302

CNN-TA - LSTM 0.0010461

CNN-TA - MLP 0.0000013

2007-2012

CNN-TA - BaH 0.0013547

CNN-TA - LSTM 0.0755492

CNN-TA - MLP 0.0463610

21

5.9. Future Directions

Even though the performance of the model is promising, more improvements can still

be achieved. The model might perform better if CNN structural parameters are optimized.

Evolutionary algorithms for model optimization may enhance the network performance.

Similarly, selecting the proper image size, window size, technical analysis optimization can

improve the overall performance considerably. Also, data representation for ”Buy”, ”Sell”,

”Hold” points can be optimized for better trade signal generation performance.

In this study, we analyzed a long-only strategy for our algorithmic trading model. How-

ever, adapting a long-short strategy might increase the proﬁt signiﬁcantly, since there are

a lot idle times where the model is sitting on cash while waiting for a trigger Buy signal.

Similarly, based on the stock/ETF performance, a portfolio with multiple stocks/ETFs can

be dynamically allocated and enhanced overall performance with less risk can be achieved.

From a general perspective, more applications might start adapting 2-D CNN for non-

image data in the future. There are already some indications for this trend for time series

forecasting [61, 62, 63], gait recognition through radar signals [64] and malware classiﬁcation

[65, 66]. Following these recent developments, in the near future, we might expect similar

implementations in other ﬁelds to start utilizing image-based CNN.

6. Conclusion

In this study, we utilized a 2-D Deep Convolutional Neural Network model to be used

with ﬁnancial stock market data and technical analysis indicators for developing an algo-

rithmic trading system. In our proposed solution, we analyzed ﬁnancial time series data

and converted this data into 2-D images. In our study, we attempted to predict entry and

exit points of the time series values as ”Buy”,”Sell” and ”Hold” marks for proﬁtable trades.

We used Dow Jones 30 stock prices and ETFs as our ﬁnancial time series data. The results

indicate this novel approach performs very well against Buy & Hold and other models over

long periods of out-of-sample test periods. For future work, we will use more ETFs and

stocks in order to create more data for the deep learning models. We will also analyze the

correlations between selected indicators in order to create more meaningful images so that

the learning models can better associate the Buy-Sell-Hold signals and come up with more

proﬁtable trading models.

7. Acknowledgement

This study was funded by The Scientiﬁc and Technological Research Council of Turkey

(TUBITAK) under grant number 215E248.

8. Appendix

8.1. Relative Strength Index (RSI)

Relative Strength Index (RSI) is an oscillator type technical analysis indicator that shows

the historical strength and weakness of stock prices. As stock prices change, RSI values

22

oscilate between 0 and 100 which indicates whether the stock prices are in the overbought

or oversold region. The most common usage of RSI indicator and its interpretation works

as follows: If the value is over 70, the stock is considered to be in the overbought region.

Meanwhile, if the value is under 30, the stock is assumed to be in the oversold region.

Equation for calculating the RSI value is provided in Equation 12.

RSI = 100 −100

1 + averagegain

averageloss

(12)

8.2. Williams %R

Williams %R is a momentum based technical indicator that also determines overbought

and oversold conditions for stock prices. It oscillates between -100 and 0 values. The

corresponding logic for Williams %R is exactly the same as RSI. If the value is under -80,

it is interpreted that stock prices are in the oversold region. In contrast, if the value is over

-20, the stock price is considered to be in the overbought region. Equation 13 shows how

Williams %R value is calculated.

R=max(high)−close

max(high)−min(low)∗ −100 (13)

8.3. Simple Moving Average (SMA)

Simple Moving Average (SMA) shows the moving average of the prices for a given period.

In its most widely accepted interpretation, the intersection of the SMA values with diﬀerent

interval values are used to determine the trend direction. As a result, multiple SMAs can

be combined to be used together, or one single SMA value can be used in conjunction with

the underlying stock, i.e. if the stock price is higher than the SMA (for instance 50 day), it

is assumed that the stock is in uptrend, indicating the stock price will continue to increase

(Buy trigger), whereas if the stock price is lower than the SMA, it is assumed that the stock

is in downtrend, indicating the stock price will decrease (Sell trigger). Calculation of SMA

is summarized in Equation 14.

SM A(M, n) =

a+n

X

k=a+1

M(k)

n(14)

8.4. Exponential Moving Average (EMA)

Exponential Moving Average (EMA) is a type of moving average indicator that shows

moving average of the prices, emphasizing more for latest days. Latest data has more

weight when calculating the moving average. Importance of the latest data is exponentially

increasing in EMA calculations. Equation 15 illustrates the calculation of EMA of the stock

prices.

(M(t)−EM A(M, t −1, τ )).2

τ+ 1 +EM A(M, t −1, τ) (15)

23

8.5. Weighted Moving Average (WMA)

Weighted Moving Average (WMA) is another type of moving average indicator that is the

same as exponential moving average. The only diﬀerence is the importance of the close price

is decreasing linearly when moving back to the past. On the other hand, the signiﬁcance of

the close price of stock is decreasing exponentially in EMA. Equation 16 shows how WMA

is calculated.

W M A(M, n) = S um of W eig hted Aver ages

Sum of W eight (16)

8.6. Hull Moving Average (HMA)

Hull Moving Average (HMA) is a type of moving average indicator that reduces the lag

associated with SMA. EMA and WMA tries the reduction of lag using more emphasis on the

latest data. HMA improves this reduction of the lag and gets better results when compared

with EMA and WMA. Equation 17 exhibits the calculation of HMA.

W M A(M, n) = W M A(2 ∗W M A(n

2)−W M A(n)), sqrt(n) (17)

8.7. Triple Exponential Moving Average

Triple Exponential Moving Average (TEMA) is a type of EMA indicator that provides

the reduction of minor price ﬂuctuations and ﬁlters out volatility. It can be calculated as

follows:

(3 ∗EM A −3∗EMA(EMA)) + EMA(EMA(EMA)) (18)

8.8. Commodity Channel Index (CCI)

Commodity Channel Index (CCI) is an indicator that compares current prices and the

average price over a period of time. It oscillates mostly (%75) between -100 and 100 values.

%25 of time period, indicator passes its range values. Equation 19 and Equation 20 show

the calculations for CCI.

CCI =T ypical P rice −20 P eriod S MA of T P

.015 ∗Mean Deviation (19)

T ypicalP r ice(T P ) = H igh +Low +Close

3(20)

8.9. Chande Momentum Oscilator Indicator (CMO)

The Chande Momentum Oscillator (CMO) is a type of momentum indicator that is

similar to RSI and Stochastic Oscillator. It oscillates between -100 and 100. If the indicator

value is over 50, it is interpreted that stock prices are in the overbought region. If the value

is under -50, it is commonly considered that stock prices are in the oversold region. The

formula of the indicator is illustrated in Equation 21. Suis the sum of the momentum of up

days and Sdis the sum of the momentum of down days.

24

CMO = 100 ∗(Su−Sd)

(Su+Sd)(21)

8.10. Moving Average Convergence and Divergence (MACD)

Moving Average Convergence and Divergence (MACD) is a technical indicator that shows

the trend of the stock prices. If MACD line crosses signal lines in upward direction, it is

predicted that stock prices will increase. In contrast, if MACD line crosses signal lines

in downward direction, it is interpreted that stock prices will decrease. Equation 22 and

Equation 23 show the calculations of MACD and Signal Lines.

MACD Line : (12 Day EMA −26 Day EM A) (22)

Signal Line : 9 Day EMA of M ACD Line (23)

8.11. Percentage Price Oscillator (PPO)

Percentage Price Oscillator (PPO) is similar to MACD. The calculation of the PPO and

Signal Line of PPO are illustrated in Equation 24 and Equation 25.

PPO =(12 Day EMA −26 Day EM A)

26 Day EMA ∗100 (24)

Signal Line : 9 D ay E M A of P P O (25)

8.12. Rate of Change (ROC)

Rate of Change is a technical indicator that illustrates the speed of price change over a

period of time. Equation 26 shows the calculation of the formula.

RoC =(Latest Close −P revious C lose)

(P revious C lose)∗100 (26)

8.13. Chaikin Money Flow Indicator (CMFI)

Chaikin Money Flow (CMF) is a technical indicator that is used to measure Money Flow

Volume over a period of time. Indicator’s value ﬂuctuates between 1 and -1. If the value

is closer 1, it is interpreted that buying pressure is higher. On the contrary, if the value

is closer -1, it is interpreted that selling pressure is higher. Equation 27, Equation 28 and

Equation 29 illustrate the calculation of CMFI.

Multiplier =((Close −Low)−(High −Close))

(High −Low)(27)

M oney F low V olume (M F V ) = V olume ∗M ultiplier (28)

21 P eriod CM F =21 P eriod Sum of M F V

21 P eriod Sum of V olume (29)

25

8.14. Directional Movement Indicator (DMI)

Directional Movement Indicator is a technical indicator that shows the trend’s strength

and direction. It consists of three seperate indicators: Average Directional Index (ADX),

Plus Directional Indicator (+DI) and Minus Directional Indicator (-DI). DMI oscillates 0 and

100 values. Algorithm 3, Equation 27, Equation 28 and Equation 29 show the calculation

of DMI.

Algorithm 3 Calculating DMI

1: procedure DMI()

2: UpM ove =CurrentH igh −P reviousHigh

3: DownM ove =CurrentLow −P reviousLow

4: If (UpM ove > DownM ove and U pMove > 0)

5: then return (+DMI) = U pM ove,

6: else return (+DM I ) = 0

7: If (DownM ove > Upmove and DownMove > 0)

8: then return (−DMI) = DownMove,

9: else return (−DM I ) = 0

+DI = 100 ∗EM A(+DMI

Average T rue Range ) (30)

−DI = 100 ∗EM A(−DMI

Average T rue Range ) (31)

ADX = 100 ∗EM A(Absolute V alue of (+DI − −DI

+DI +−DI )) (32)

8.15. Parabolic Sar

Parabolic SAR (SAR) is a technical analysis indicator that is used to determine points

of potential stops and reverses. Current SAR is calculated with three elements; Previous

SAR (PSAR), Extreme point (EP) and Acceleration Factor (AF). Previous SAR is a SAR

value for the previous period. EP is the highest high of the current uptrend or the lowest

low of the current downtrend. AF explains the sensitivity of the SAR. AF begins at .02 and

increases by .02 every time when EP rises in a Rising SAR. AF decreases by .02 every time

when EP falls in a Falling SAR. Equation 33 shows the calculation of Rising Parabolic SAR.

Falling Parabolic SAR is calculated as in Equation 34.

P SAR +P revious AF (P revious E P +P S AR) (33)

P SAR −P revious AF (P SAR −P rev ious E P ) (34)

26

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