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Stock Market Prediction on High-Frequency Data Using Generative Adversarial Nets

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Stock price prediction is an important issue in the financial world, as it contributes to the development of effective strategies for stock exchange transactions. In this paper, we propose a generic framework employing Long Short-Term Memory (LSTM) and convolutional neural network (CNN) for adversarial training to forecast high-frequency stock market. This model takes the publicly available index provided by trading software as input to avoid complex financial theory research and difficult technical analysis, which provides the convenience for the ordinary trader of nonfinancial specialty. Our study simulates the trading mode of the actual trader and uses the method of rolling partition training set and testing set to analyze the effect of the model update cycle on the prediction performance. Extensive experiments show that our proposed approach can effectively improve stock price direction prediction accuracy and reduce forecast error.
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Research Article
Stock Market Prediction on High-Frequency Data Using
Generative Adversarial Nets
Xingyu Zhou ,1Zhisong Pan ,1Guyu Hu ,1Siqi Tang,1and Cheng Zhao1,2
1Army Engineering University of PLA, Nanjing 210007, China
2Anhui Provincial Key Laboratory of Network and Information Security, Anhui Normal University, Wuhu 241003, China
Correspondence should be addressed to Zhisong Pan; hotpzs@hotmail.com
Received 6 November 2017; Revised 21 January 2018; Accepted 13 February 2018; Published 15 April 2018
Academic Editor: Qian Zhang
Copyright ©  Xingyu Zhou et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Stock price prediction is an important issue in the nancial world, as it contributes to the development of eective strategies for
stock exchange transactions. In this paper, we propose a generic framework employing Long Short-Term Memory (LSTM) and
convolutional neural network (CNN) for adversarial training to forecast high-frequency stock market. is model takes the publicly
available index provided by trading soware as input to avoid complex nancial theory research and dicult technical analysis,
which provides the convenience for the ordinary trader of nonnancial specialty. Our study simulates the trading mode of the
actual trader and uses the method of rolling partition training set and testing set to analyze the eect of the model update cycle on
the prediction performance. Extensive experiments show that our proposed approach can eectively improve stock price direction
prediction accuracy and reduce forecast error.
1. Introduction
Predictingstockpricesisanimportantobjectiveinthe
nancial world [–], since a reasonably accurate prediction
has the possibility to yield high nancial benets and hedge
against market risks. With the rapid growth of Internet
and computing technologies, the frequency for performing
operations on the stock market had increased to fractions of
seconds [, ]. Since year of  the BM&F Bovespa (the
Brazilian stock exchange) has worked in high-frequency, and
the number of high-frequency operations has grown from
.% in  to .% in . Aldridge and Krawciw []
estimate that in  high-frequency trading on average ini-
tiated %–% of trading volume in equities and %–%
of volume in foreign exchange and commodities. ese
percentages suggest that the high-frequency stock market is
aglobaltrend.
Inmostcases,theforecastresultsareassessedfromtwo
aspects: the rst is forecast error (chiey the RMSE (Root
Mean Square Error) or RMSRE (Root Mean Square Relative
Error)) between real price and forecast value; the second is
direction prediction accuracy, which means the percentage
of correct predictions of price series direction, as upward and
downward movements are what really matters for decision-
making. Even small improvements in predictive performance
can be very protable [, ].
However, predicting stock prices is not an easy work, due
to the complexity and chaotic dynamics of the markets and
the many nondecidable, nonstationary stochastic variables
involved []. Many researchers from dierent areas have
studied the historical patterns of nancial time series and
have proposed various methods for forecasting stock prices.
In order to achieve promising performance, most of these
ways require careful selection of input variables, establishing
predictive model with professional nancial knowledge, and
adopting various statistical methods for arbitrage analysis,
which makes it dicult for people outside the nancial eld
to use these methods to predict stock prices [–].
Generative adversarial network (GAN) was introduced
by Goodfellow et al. [], where images patches are generated
from random noise using two networks trained simultane-
ou sly. Sp e cica l ly, in GAN a d iscrim inat ive ne t learns to
distinguish whether a given data instance is real or not, and
a generative net learns to confuse by generating high
quality data. Although this approach has been successful and
applied to a wide range of elds, such as image inpainting,
Hindawi
Mathematical Problems in Engineering
Volume 2018, Article ID 4907423, 11 pages
https://doi.org/10.1155/2018/4907423
Mathematical Problems in Engineering
semantic segmentation, and video prediction [–], as far
as we know, it has not been used for stock forecasting.
is work uses basic technical index data as an input
variable, which can be acquired directly from trading so-
ware,sothatpeopleoutsidethenancialeldcanpredict
stock price through our method easily. is study introduces
forecast error loss and direction prediction loss and shows
that generative adversarial training [] may be successfully
employed for combining these losses to produce satisfying
predict results, and we call this prediction architecture GAN-
FD (GAN for minimizing forecast error loss and direction
predictionloss).Forthepurposeofconformingtothe
practice of actual transactions, this work carries out rolling
segmentation on training set and testing set of the raw data,
and we will illustrate it in detail in the experimental section.
Overall, our main contributions are twofold: () we
adapted generative adversarial network for the purpose of
price prediction, which constitutes to our knowledge the
rst application of adversarial training to stock market, and
extensive experiments show that our prediction model can
achieve remarkable results and () we carry out rolling
segmentation on training set and testing set of the raw data to
investigate the eect the of model parameter update cycle on
the stock forecast performance, and the experimental results
show that smaller model update cycle can advance prediction
performance.
In the remainder of this paper, we begin with a review
of the literature on which algorithms have been used for the
nancial market prediction. en we formulate the problem
and propose our general adversarial network framework.
Furthermore, in the experiments section, we presented the
experimental analysis with the proposed model, as well as a
comparison between the obtained results with those given by
classical prediction models. Finally, conclusions and possible
extensions are discussed.
2. Related Work
is section introduce the related work from the stock market
prediction method and the generative adversarial network.
2.1. Stock Market Prediction Method. According to the re-
search developed in this eld, we can classify the techniques
used to solve the stock market prediction problems to
twofold.
e rst category of related work is econometric models,
which includes classical econometric models for forecasting.
Common methods are the autoregressive method (AR), the
moving average model (MA), the autoregressive moving
average model (ARMA), and the autoregressive integrated
moving average (ARIMA) [–]. Roughly speaking, these
models take each new signal as a noisy linear combination of
the last few signals and independent noise terms. However,
most of them rely on some strong assumptions with respect
to the noise terms (such as i.i.d. assumption, -distribution)
and loss functions, while real nancial data may not fully
satisfy these assumptions. By introducing a generalized
autoregressive conditional heteroscedastic (GARCH) model
for conditional variances, Pellegrini et al. [] apply ARIMA-
GARCH model to the prediction of nancial time series.
e second category involves so computing based mod-
els. So computing is a term that covers articial intelligence
which mimics biological processes. ese techniques include
articial neural networks (ANN) [, ], fuzzy logic (FL)
[], support vector machines (SVM) [, ], particle swarm
optimization (PSO) [], and many others. Many authors
have tried to deal with fuzziness along with randomness in
option pricing models [, ]. Carlsson and Full´
er [] were
the rst to study the fuzzy real options and avaneswaran
et al. [] demonstrated the superiority of the fuzzy fore-
casts and then derived the membership function for the
European call price by fuzzifying the interest rate, volatility,
and the initial value of the stock price. Recently there has
been a resurgence of interest in deep learning, whose basic
structure is best described as a multilayer neural network
[]. Some literatures have established various models based
on deep neural networks to improve the prediction ability
of high-frequency nancial time series [, ]. e ability
of deep neural networks to extract abstract features from
data is also attractive, Chong et al. [] applied a deep
feature learning-based stock market prediction model, which
extract information from the stock return time series without
relying on prior knowledge of the predictors and tested
it on high-frequency data from the Korean stock market.
Chen et al. [] proposed a double-layer neural network for
high-frequency forecasting, with links specially designed to
capture dependence structures among stock returns within
dierent business sectors. ere also exist a few studies
that apply deep learning to identication of the relationship
betweenpastnewseventsandstockmarketmovements[
].
However,toourknowledge,mostofthesemethods
require expertise to impose specic restrictions on the input
variables, such as combining related stocks together as entry
data [], inputting dierent index data to dierent layers
of the deep neural network [], and converting news text
into structured representation as input []. In contrast, our
proposed forecasting model directly uses the data provided
by the trading soware as input, which reduce the barrier for
ordinary investors.
2.2. Generative Adversarial Network. Generative adversarial
network (GAN) is a framework for estimating generative
modelsviaanadversarialprocess,inwhichwesimultane-
ously train two models: a generative model that capturesthe
data distribution and a discriminative model that estimates
the probability that a sample came from the training data
rather than . e training procedure for is to maximize
the probability of making a mistake. is framework
corresponds to a minimax two-player game. In the space of
arbitrary functions and D, a unique solution exists, with
recovering the training data distribution and equal to
. everywhere []. While and are dened by multilayer
perceptrons in [], most researches recently constructed
and on the basis of Long Short-Term Memory (LSTM)
[] or convolutional neural network (CNN) [] for a large
variety of application.
Mathematical Problems in Engineering
XG
YY
Y
X1,X2,...,XT
LSTM
internal
unit
LSTM
internal
unit
LSTM
internal
unit
Y
1,Y
2,...,Y
T,
Y
T+1
Y
1,Y
2,...,Y
TY
1,Y
2,...,Y
T,Y
T+1
D
Input
sequence Conv.
Conv. Conv. FC
FC
Real
Predicted
F : GAN-FD architecture. e generator ()is founded on LSTM, which applies to predicting
𝑇+1. e discriminator ()is based on
CNN for the purpose of estimating the probability whether a sequence is real (Y)or being predicted (
Y).Conv. means convolutional layer,
FC is an abbreviation for fully connected layer. e structure of and can be adjusted according to the specic application.
LSTM is a basic deep learning model and capable of
learning long-term dependencies. A LSTM internal unit is
composed of a cell, an input gate, an output gate, and a
forget gate. LSTM internal units have hidden state augmented
with nonlinear mechanisms to allow state to propagate
withoutmodication,beupdated,orbereset,usingsimple
learned gating functions. LSTM work tremendously well on
various problems, such as natural language text compression,
handwriting recognition, and electric load forecasting.
CNN is a class of deep, feed-forward articial neural net-
works that has successfully been applied to analyzing visual
imagery. A CNN consists of an input layer and an output
layer, as well as multiple hidden layers. e hidden layers of a
CNN typically consist of convolutional layers, pooling layers,
fully connected layers, and normalization layers. CNN also
has many applications such as image and video recognition,
recommender systems, and natural language processing.
Although there are a lot of literatures forecast stock price
by using LSTM model, to the best of our knowledge, this
paper is the rst to adopt GAN to predict stock prices.
e experimental part (Section .) compares the prediction
performances between GAN-FC and LSTM.
3. Forecasting with High-Frequency Data
In this section, we illuminate the details of the generative
adversarial network framework for stock market forecasting
with high-frequency data.
3.1. Problem Statement. Under the high-frequency trading
environment, high-quality one-step forecasting is usually
of great concern to algorithmic traders, providing signi-
cant information to market makers for risk assessment and
management. In this article, we aim to forecast the price
movement of individual stocks or the market index one step
ahead, based solely on their historical price information. Our
problem can be mathematically formalized as follows.
Let X𝑡represent a set of basic indicators and 𝑡denote
the closing price of one stock for a -minute interval at
time ( = 1,2,...,),whereis the maximum lag
of time. Given the historical basic indicators information
X(X={X1,X2,...,X𝑇})and the past closing price Y(Y=
{1,2,...,𝑇}), our goal is to predict the closing price 𝑇+1
for the next -minute time interval. ere are literatures that
examined the eects of dierent [, , ], but, in this work,
we just set to  because each trading day contains -
minute intervals in the China stock exchanges.
3.2. Prediction Model. e deep architecture of the proposed
GAN-FD model is illustrated as in Figure . Since the stock
dataisatypicaltimeseries,wechooseLSTMmodel,which
is widely applied to time series prediction, as the generative
model to predict output
𝑇+1 based on the input data X;
that is,
𝑇+1 =(X).()
e discriminative model is based on the CNN
architecture and performs convolution operations on the
one-dimensional input sequence in order to estimate the
probability whether a sequence comes from the dataset (Y=
{1,2,...,𝑇,𝑇+1 }) or being produced by a generative
model (
Y={1,2,...,𝑇,
𝑇+1}).
Our main intuition on why to use an adversarial loss
is that it can simulate the operating habits of nancial
traders. An experienced trader usually predicts stock price
through the available indicator data, which is the work of the
generative model , and then judges the correct probability
of his own forecast with the previous stock price, as the
discriminative model does.
It is noteworthy that the structure of and in GAN-
FD can be adjusted according to specic application, and
the experimental part in this paper just proposed simple
and framework (Section .) for stock prediction. It is
reasonable to believe that ne-tuning the structure of and
can improve the predictive performance.
3.3. Adversarial Training. e training of the pair (,)
consists of two alternated steps, described below. For the sake
of clarity, we assume that we use pure SGD (minibatches of
size ), but there is no diculty to generalize the algorithm
to minibatches of size by summing the losses over the
samples.
Training (let (X,Y)be a sample from the dataset). In order
to make the discriminative model as “confused” as possible,
the generative model should reduce the adversarial loss in
the sense that will not discriminate the prediction correctly.
Classifying Yinto class  and
Yinto class , the adversarial
loss for is 𝐺
adv
Y=sce 
Y,1, ()
Mathematical Problems in Engineering
where sce is the sigmoid cross-entropy loss, dened as
sce (A,B)=−
𝑖𝑖log sigmoid 𝑖
+1−𝑖log 1sigmoid 𝑖. ()
However, in practice, minimizing adversarial loss alone
cannot guarantee satisfying predictions. Imagine that could
generate samples to “confuse” ,withoutbeingcloseto
𝑇+1,
and then will learn to discriminate these samples, leading
to generate other “confusing” samples, and so on. To address
this problem, the generative model ought to decrease the
forecast error loss; that is, 𝑝loss
𝑝Y,
Y=Y
Y𝑝()
where =1or =2.
Furthermore, as mentioned above, stock price direction
prediction is crucial to trading, so we dene direction pre-
diction loss function dpl:
dpl Y,
Y=sgn
𝑇+1 −𝑇−sgn 𝑇+1 −𝑇()
where sgn represents sign function.
Combining all these losses previously dened with dier-
ent parameters adv,𝑝,anddpl ,weachievethenallosson
:
𝐺(X,Y)=adv 𝐺
adv
Y+𝑝𝑝Y,
Y
+dpl dpl Y,
Y. ()
en we perform one SGD iteration on to minimize
𝐺(X,Y)whilekeepingtheweightsofxed.
Training (let (X,Y)be a dierent data sample). Since the
role of is just to determine whether the input sequence is
Yor
Y, the target loss is equal to the adversarial loss on D.
Whilekeepingtheweightsofxed, we perform one SGD
step on to minimize the target loss:
𝐷(X,Y)=𝐷
adv Y,
Y
=sce 
Y,0+sce Y,1. ()
We train the generator and discriminator iteratively. e
entire process is summarized in Algorithm , with minibatch-
es of size .
() Set the learning rates 𝐷and 𝐺, and parameters
adv,𝑝,dpl ;
() Initialize weights 𝐷and 𝐺.
() while not converged do
() Update the generator :
() Get new data samples (X(1),Y(1)), (X(2),
Y(2)),...,(X(𝐾),Y(𝐾))
() 𝐺=𝐺−𝐺
𝐾
𝑖𝐺(X(𝑖),Y(𝑖))
𝐺
() Update the discriminator :
() Get new data samples (X(1),Y(1) ), (X(2),
Y(2)),...,(X(𝐾),Y(𝐾))
() 𝐷=𝐷−𝐷
𝐾
𝑖𝐷(X(𝑖),Y(𝑖))
𝐷
() end while
A : Training GAN-FD.
4. Experiments
4.1. Dataset. Next, we evaluate the performance of the pro-
posed method based on the China stock market, ranging
from January , , to December , . ere are totally
 trading days and each day contains -minute intervals,
corresponding to  time points. ese stocks selected
for the experiment should conform to three criteria: rst,
they should be the constituent stock of  (the CSI
 is a capitalization-weighted stock market index designed
to replicate the performance of  stocks traded in the
Shanghai and Shenzhen stock exchanges); second, they were
not suspended during the period we just mentioned, in case
accidentaleventsbringaboutsignicantimpactontheirprice
and aect forecast results; third, their closing prices in the
start time, that is, January , , are above  to ensure
the volatility for high-frequency exchange. is leaves 
stocks in the sample, which are listed in Table . e number
of increasing directions and decreasing directions for each
stock’s closing price per minute is also shown in Table , and
their numbers are relatively close. e historical data was
obtained from the Wind Financial Terminal, produced by
Wind Information Inc. (the Wind Financial Terminal can be
downloaded from http://www.wind.com.cn).
Many fund managers and investors in the stock market
generally accept and use certain criteria for technical indi-
cators as the signal of future market trends [, ]. is
work selects  technical indicators as feature subsets by
the review of domain experts and prior researches; that is,
the input data Xat each moment (e.g., X𝑇)consistsof
basic indicators that can be obtained directly from almost all
trading soware. ese basic indicators are listed in Table ,
and their parameters are using the default value of the Wind
Financial Terminal. As mentioned above, Yis dened as the
closing price at each moment.
Mostoftherelatedarticlesusethetraditionaldata
partitioning method; that is, the entire dataset is directly split
into training set and testing set [, , , ]. However,
Mathematical Problems in Engineering
T : e sample stocks and their number of increasing direc-
tions and decreasing directions.
ID Stock code Increase Decrease
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SZ  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
 .SH  
the trading style of the stock market changes frequently;
for example, investors sometimes prefer stocks with high
volatility and sometimes tend to invest in technology stocks.
erefore, we should update the model parameters regularly
to adapt to the change of market style. In order to make
experiments closer to real transactions, we carry out rolling
T : Basic indicators for prediction.
Indicators
Opening price
Maximum price
Minimum price
Trading volume
Turnov e r
Bias
Bollinger bands
Directional movement index
Exponential moving averages
Stochastic index
Moving averages
MACD
Relative strength index
Dataset
M
M
M
N
N
N
F : Rolling segmentation on training set and testing set. e
green bar represents the entire dataset, the blue bar represents the
training set for a round experiment, and the yellow bar represents
the corresponding testing set.
segmentation on training set and testing set of the experi-
mental data. As Figure  shows, in the beginning, we select
the rst days as training set, and the next days play the
role of testing set. Aer the rst round of experiments, we
roll forward the time window for days, that is, choosing
the (+1)th day to the (+)th day as training set and the
(++1)th day to the (+2)th day as testing set. Repeat
until all the data has been experimented. In other words, this
can be regarded as the model update cycle, and is the
size of the corresponding training data.
4.2. Network Architecture. Given that the LSTM generator
takes on the role of prediction and requires more accurate
calculations of values than the CNN discriminator, we set the
learning rate 𝐺to . and 𝐷to .. e LSTM cell in
contains  internal (hidden) units and the parameters
are initialized following the normal distribution N(0,1).
e architecture of discriminative model is presented in
Table . We train GAN-FD with =2weighted by adv =
𝑝=dpl =1.
4.3. Benchmark Methods. To e v a l u a t e t h e p erformanc e of
our proposed method, we include three baseline meth-
ods for comparison. e rst model is ARIMA (1,1,1)-
GARCH(1,1), a tted ARIMA model that forecasts future
Mathematical Problems in Engineering
T : Network architecture of discriminative model .
Layer Conguration
Convolution  Filter 32×4×1, strides 2,LReLU
Convolution  Filter 64×4×1, strides 2,LReLU,BN
Convolution  Filter 128×4×1, strides 2,LReLU,BN
FC  , leaky ReLU
FC  , sigmoid
Optimizer: SGD; batch size: ; iterations: ; LReLU slope: ..
T : Summary of RMSRE with dierent (M,N). ese gures are the average values over the  stocks.
=5 =10 =20
=10 =20 =60 =10 =20 =60 =10 =20 =60
ARIMA-GARCH . . . . . . . . .
ANN . . . . . . . . .
SVM . . . . . . . . .
GAN-F . . . . . . . 0.0313 .
GAN-D . . . . . . . . .
LSTM-FD . . . . . . 0.0321 . .
GAN-FD 0.0098 0.0079 0.0101 0.0218 0.0111 0.0144 . . 0.0296
values of stock time series and the GARCH model forecasts
future volatilities []. e second one is articial neural
networks (ANN). e parameter optimization method and
modelarchitecturalissettingasin[],exceptthattheinput
layernodeischangedtoandthenetworkoutputsthe
predicted value instead of two patterns ( or ). e third one
issupportvectormachines(SVM).AnRBFkernelisusedand
the parameter is setting as in [].
We also inspect our GAN-FD model from several ways.
e GAN-F model is using a GAN architectural for mini-
mizing forecast error loss, with adv =
𝑝=1and dpl
=0. e GAN-D model is using a GAN architectural for
minimizing direction prediction loss, with adv =dpl =1
and 𝑝=0. e LSTM-FD model is a LSTM model aiming
at minimizing forecast error loss and direction prediction
loss, with  internal units in LSTM. Obviously, the main
dierence between LSTM-FD and GAN-FD is the presence
of adversarial training.
4.4. Evaluation Metrics. For each stock at each time ,a
prediction is made for the next time point +1based on
a specic method. Assume the total number of time points
being tested is 0; we used the following criteria to evaluate
the performance of dierent models.
(1) Root Mean Squared Relative Error (RMSRE)
RMSRE =1
0
𝑇0
𝑡=1
𝑡+1 −𝑡+1
𝑡+1 2.()
RMSREisemployedasanindicatorforthepredictivepower
or prediction agreement. A low RMSRE indicates that the
prediction agrees with the real data (the reason why this paper
uses RMSRE instead of RMSE is that RMSRE facilitates a
uniform comparison of the results of  stocks).
(2) Direction Prediction Accuracy (DPA)
DPA =100
0
𝑇0
𝑡=1𝑡,()
where
𝑡=
1if 𝑡+1 −𝑡
𝑡+1 −𝑡>0
0otherwise .()
DPA measures the percentage of accuracy relating to the
series trend. A high DPA promises more winning trades.
4.5. Results. In order to investigate the eect of the model
update cycle on the predictive performance, let {10,20,
60}and  ∈ {5,10,20}.InChinastockexchangemarket,
{5,10,20,60} days represent one week, two weeks, one
month, and one quarter.
Tables  and  show the average values of RMSRE and
DPA with dierent (,). e numbers clearly indicate that
GAN-FD and its related methods perform better than three
baseline methods in terms of RMSRE and DPA. is targeted
method GAN-F brings some improvement in RMSRE, but
it does not outperform three baseline methods in DPA.
Contrary to GAN-F, GAN-D achieves better results in DPA
but failed in RMSRE. LSTM-FD improves the results, since
it combines forecast error loss with direction prediction loss
for training. Finally the combinationof the forecast error loss,
direction prediction loss, and adversarial training, that is,
GAN-FD, achieves the best RMSRE and DPA in the majority
of scenarios.
Letustakealookattheeectsofdierent(M,N)onthe
experiment. GAN-FD obtains the maximum average DPA
(.) and the minimum average RMSRE (.) when
Mathematical Problems in Engineering
T : Summary of DPA with dierent (M,N). ese gures are the average values over the  stocks.
=5 =10 =20
=10 =20 =60 =10 =20 =60 =10 =20 =60
ARIMA-GARCH . . . . . . . . .
ANN . . . . . . . . .
SVM . . . . . . . . .
GAN-F . . . . . . . . .
GAN-D . . . . . . . . .
LSTM-FD . . . . . . 0.5546 0.5635 .
GAN-FD 0.6761 0.6956 0.6793 0.6233 0.6651 0.6687 . . 0.5753
T : e number of times about the minimum RMSRE.
=5 =10 =20
=10 =20 =60 =10 =20 =60 =10 =20 =60
ARIMA-GARCH 
ANN 
SVM 
GAN-F   18 
GAN-D 
LSTM-FD 16  
GAN-FD 31 40 33 30 33 35   19
T : e number of times about the maximum DPA.
=5 =10 =20
=10 =20 =60 =10 =20 =60 =10 =20 =60
ARIMA-GARCH 
ANN 
SVM   
GAN-F 
GAN-D         
LSTM-FD  18 15 
GAN-FD 41 38 32 26 37 35   19
(M,N) is (, ). It is interesting to note that all these
methods work better when is  than when is  or ,
with smaller RMSRE and higher DPA. is implies that very
short-term trends are best for predicting the next minutes
price. erefore, a shorter model update cycle (e.g., is )
is preferred. On the other hand, for the same , dierent
will bring about some changes to the prediction results.
From the experimental results, we suggest that should take
the value greater than . is makes intuitive sense. If the
training sample is inadequate, it would fail to train the model,
especially in the volatile stock markets. We should also notice
that when the training set is small while the testing set is
large (i.e., (M,N) is (, )), most of these methods perform
the worst, and the DPA of these methods are no better than
random guessing (i.e., %).
Table  shows the number of times for each method
to achieve the minimum RMSRE over the  stocks. It is
noticeable that the results of these three baseline methods are
all zero. GAN-FD with its related methods is obviously better
than these three baseline methods in RMSRE. Meanwhile,
GAN-FD obtains the minimum RMSRE  times, account-
ing for .% in these  scenarios ( stocks and  groups
(M,N)). e best performance appeared when (M,N)is(,
), with  stocks’ minimum RMSRE coming from GAN-FD.
Table  shows the number of times for each method to
achieve the maximum DPA over the  stocks. Compared
with the other six methods, GAN-FD achieves the maximum
DPA  times, accounting for .% in all scenarios. When
(M,N) is (, ), the maximum DPA of  stocks in all 
stocks comes from GAN-FD. Even when (M,N)is(,),
that is, the worst performance of GAN-FD cases, GAN-FD
still obtains maximum DPA in  stocks. From the above
analyses, the performance of the GAN-FD is signicantly
better than the other six ways.
e results of each representation are reported in Figures
–. We just focus on GAN-FD. As shown in Figures –,
the DPA of GAN-FD ranges around .%–.% when
is , and it slumps to .%–.% when is , which
is presented in Figures –. When is , the RMSRE of
GAN-FD over the  stocks varies between .% and .%,
Mathematical Problems in Engineering
0 0
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axis represents the stock ID.
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
0
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
0
0.1
0.2
0.3
0.4
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0.6
0.7
0.8
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0.01
0
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RMSRE
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axis represents the stock ID.
Mathematical Problems in Engineering
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
DPA
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
RMSRE
1
2
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6
8
3
5
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
DPA
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
RMSRE
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
1
2
4
6
8
3
5
7
9
10
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
DPA
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
RMSRE
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
1
2
4
6
8
3
5
7
9
10
11
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13
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
DPA
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
RMSRE
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
1
2
4
6
8
3
5
7
9
10
11
12
13
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
 Mathematical Problems in Engineering
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
DPA
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
RMSRE
ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD ARIMA-GARCH
ANN
SVM
GAN-F
GAN-D
LSTM-FD
GAN-FD
1
2
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F : DPA and RMSRE of each stock when (M,N)is(,)and-axisrepresentsthestockID.
which is lower than other six methods in most cases, while
the volatility is smaller. However, the RMSRE of GAN-FD
increases dramatically and uctuates violently when is ,
and it varies between .% and .%. is further shows
that we should reduce the model update cycle and revise
the model parameters regularly to adapt to the change of
market style.
5. Conclusion
In this paper, we propose an easy-to-use stock forecasting
model called GAN-FD, to assist more and more nonnancial
professional ordinary investors making decisions. GAN-FD
adopts  simple technical indexes as input data to avoid
complicated input data preprocessing. Based on the deep
learning network, this model achieves prediction ability supe-
rior to other benchmark methods by means of adversarial
training, minimizing direction prediction loss, and forecast
error loss. Moreover, the eects of the model update cycles on
the predictive capability are analyzed, and the experimental
resultsshowthatthesmallermodelupdatecyclecanobtain
better prediction performance. In the future, we will attempt
to integrate predictive models under multiscale conditions.
Conflicts of Interest
e authors declare that there are no conicts of interest
regarding the publication of this paper.
Acknowledgments
isworkissupportedbytheNationalKeyResearch
Development Program of China (YFB) and
the National Natural Science Foundation of China (no.
).
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... Alternative methods for training adversarial networks have included using Ensemble LSTM with CNN on stock indices. Benefits of this approach include adversarial training, less direction prediction loss, and forecast error loss; it can aid in high-frequency stock forecasting [24]. When combined, XG-Boost and LSTM can outperform each component alone when used to high-dimensional time series data for feature identification and stock price forecasting, respectively. ...
Conference Paper
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These days, the majority invest their money in financial products. Every country on Earth is affected by the financial operations. A stock market is any platform that enables the issuance and businesses of stocks in an organized fashion, this can also occur physically or digitally. Uncertainty is introduced into stock prices by the numerous rules and regulations that regulate the financial processes inherent to the stock market. There are many risks in the financial market, but at the same time, it also offers many opportunities for profits. The proposed system consists of the following steps: preprocessing, feature selection, and model training. Data preparation is all about the enhancement of the selected data. Feature selection in stock market movements forecasting is a process of selecting the relevant features/variables from the dataset. It helps to reduce dimensionality, prevents overfitting, and improves forecast
... Notably, RNN variants such as long short-term memory (LSTM) networks and gated recurrent units (GRUs) have been specifically employed to forecast U.S. stock market volatility [61], while CNNs have been used to predict future prices in the Chinese and Indian stock markets [15,50]. GANs have been proposed for price prediction in indices like the FTSE MIB, CSI 300, and S&P 500 [72,73,86]. Hybrid models that combine neural networks with traditional machine learning techniques have also shown promise in enhancing prediction accuracy [45,56,83]. ...
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... Similarly, the authors of [41] combined Bi-LSTM with a CNN, showing a 9% improvement in prediction performance compared with single pipeline models. The authors of [42] proposed a simple GAN model with LSTM as a generator and a CNN as the discriminator, incorporating 13 technical indicators, and demonstrated that the generative adversarial network (GAN) outperformed other models like LSTM, artificial neural network (ANN), support vector machine (SVM), and ARIMA for stock price prediction. Ref. [43] used a GAN with an LSTM generator and a multiple perceptron (MLP) discriminator, outperforming traditional a model based on RMSE and MAE. ...
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... f e-mail: anton.albino@fieb.org.br of domains [11][12][13]. In the finance domain, applications of GANs include financial data generation [12,14,15], stock market prediction [16,17], credit scoring [18] and fraud detection [19,20]. In the image processing domain, GANs are used notably for image superresolution (ISR) [21,22] that can also improve early medical diagnosis in clinical pathology [23] to name a few. ...
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