Finance, Markets and Valuation
Corresponding author
Javier Oliver Muncharaz
Received: 2 Oct 2020
Revised: 15 Nov 2020
Accepted: 19 Dec 2020
Finance, Markets and
ISSN 2530-3163.
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Comparing classic time series models and the LSTM
recurrent neural network: An application to S&P 500
Comparativa de los models clásicos de series temporales
con la red neuronal recurrente LSTM: Una aplicación a las
acciones del S&P 500
Javier Oliver Muncharaz
Departamento de Economía y Ciencias Sociales, Universidad Politécnica de Valencia. Valencia,
España. Email:
JEL: G12; G17; C45
In the financial literature, there is great interest in the prediction of stock prices. Stock prediction is nec-
essary for the creation of dierent investment strategies, both speculative and hedging ones. The ap-
plication of neural networks has involved a change in the creation of predictive models. In this paper,
we analyze the capacity of recurrent neural networks, in particular the long short-term recurrent neural
network (LSTM) as opposed to classic time series models such as the Exponential Smooth Time Series
(ETS) and the Arima model (ARIMA). These models have been estimated for 284 stocks from the S&P 500
stock market index, comparing the MAE obtained from their predictions. The results obtained confirm a
significant reduction in prediction errors when LSTM is applied. These results are consistent with other
similar studies applied to stocks included in other stock market indices, as well as other financial assets
such as exchange rates.
Keywords: Recurrent Neural Network; Long short-term neural network; S&P 500; Arima
En la literatura financiera existe un gran interés por la predicción de precios bursátiles que es necesario
para la creación de diferentes estrategias de inversion, tanto especulativas como de cobertura. La apli-
cación de las redes neuronales ha supuesto un cambio en la creación de modelos de predicción. En este
trabajo se analiza la capacidad que tienen las redes neuronales recurrentes, en concreto la long short-
term recurrent neural network (LSTM) frente a modelos de series temporales clásicos como el Exponen-
tial Smooth Time Series (ETS) y el modelo Arima (ARIMA). Para ello se ha estimado dichos modelos para
284 acciones pertenecientes al índice bursátil S&P 500, comparando el MAE obtenido de sus prediccio-
nes, con el modelo LSTM. Los resultados obtenidos confirman una reducción importante de los errores
de predicción. Estos resultados son coincidentes con otros estudios similares aplicados a acciones de
otros índices bursátiles así como a otros activos financieros como los tipos de cambio.
Cómo citar este artículo: Oliver Muncharaz, J. (2020) Comparing classic time series models and the
LSTM recurrent neural network: An application to S&P 500 stocks. Finance, Markets and Valuation
6(2), pp. 137–148.
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Keywords: Redes neuronales recurrentes; Long short-term neural network; S&P 500; Arima
1 Introduction
The prediction of stock returns has been widely studied in the financial literature. One of the
main objectives is the construction of stock portfolios. In some cases, these portfolios are
constructed by applying dierent optimisation algorithms based on the classic Markowitz
model (García, González-Bueno, & Oliver, 2015). Some optimisation algorithms, such as the
NSGA-II, allow the construction of these portfolios taking into account more than the two classic
return-risk dimensions (W. Chen, Zhang, Mehlawat, & Jia, 2021; García, González-Bueno, Oliver,
& Tamoši
e, 2019). Other algorithms, such as genetic algorithms together with heuristic
techniques allow good solutions to be found in an NP-hard problem (Ahn, Lee, Ryou, & Oh, 2020;
García, Guijarro, & Oliver, 2018). Other studies try to find relations between sustainability and
stock market portfolios or indexes. Thus, for example, Arribas, Espinós-Vañó, García, and Oliver
(2019) analyse the composition and selection of responsible companies for the construction
of portfolios and investment funds, while Espinós-Vañó, García, and Oliver (2018) analyse the
so-called sustainable stock market indexes to determine whether they can be an investment
alternative to traditional stock market indexes.
Stock prediction is also applied to speculate with the price evolution of financial assets.
Predictive models can be classified into linear and non-linear models. To the first group belong
time series models such as autoregressive integrated moving average, exponential smooth
models and generalized autoregressive conditional heteroskedasticity, among others. Neural
networks are assigned to a second group. Given that the stock returns are not stationary and
present long-term dependence (Barkoulas & Baum, 1996), this second group of models have
shown to obtain more accuracy and a reduction of errors prediction with respect to linear
In the last few decades, neuronal networks have evolved from the initial models of Hebb,
which proposed the first rules of learning processes between neurons, Widrow and Ho with
their model Adaline, and Rosenblatt, which proposed the well-known perceptron. There are
many works related to the prediction of stock prices and their trends applying models based
on artificial neuronal networks. In Qiu and Song (2016), for example, the authors present the
analysis of the prediction or the direction of stock price index for the Nikkei 225 stock market
index. In this case, they use a backpropagation neural network with two dierent types of inputs
to determine what kind of information improves results. The result suggests that the network
is able to select those variables that are suitable for the model. Moghaddam, Moghaddam, and
Esfandyari (2016) apply the same type of network for the prediction of the Nasdaq stock index
using historical short term data as inputs (between four and nine days). In García, Guijarro,
Oliver, and Tamoši
e (2018) the authors apply a neural network to predict the trend of the
German Dax-30 stock index.
In recent years, recurrent neural networks have been widely used for the analysis of time
series with high time dependency, such as stock returns. These types of networks are based
on Rumelhart’s work on error backpropagation (Rumelhart, Hinton, & Williams, 1986) and
Hopfield’s networks (Hopfield & Tank, 1985). Some works make a comparative analysis between
some already known neural networks against the recurrent neural networks as for example
in Saad, Prokhorov, and Wunsch (1998). The authors compare the time delay neural network
(TDNN), probabilistic neural network (PNN) and a recurrent neural network to predict short-term
stock trends. The conclusion is that the TDNN has the capability to dynamically incorporate past
Javier Oliver Muncharaz 138
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
data to internal recurrence, and is the most powerful network among those analysed, although
it presents certain complexity regarding its implementation and memory requirement.
On the other hand, Yoshihara, Fujikawa, Seki, and Uehara (2014) compare RNN with another
machine learning methodology, the support vector machine (SVM) model. They analyse trend
market prediction on Nikkei companies. In this case, in addition to incorporating numerical
inputs into the models, information on dierent economic and financial events is introduced
(news reported by newspapers). The advantage of deep learning is its ability to automatically
construct dierent features from data as well as pattern recognition. The results from RNN were
compared with SVM, and present the lowest error rate. This study shows that recurrent models
are more eective in capturing past events that are significant with respect to long-term eects.
Other studies also confirm these results, like the paper by Rather, Agarwal, and Sastry
(2015) who analyse 25 stock returns from Bombay stock exchange indicating that this model is
capable of capturing non-linear patterns more eiciently than classical models. In this case it is
concluded that the RNN learning process improves as it needs to look for smaller weights. da
Silva, Spatti, Flauzino, Liboni, and dos Reis Alves (2016) analyse stocks in the Bovespa index,
which is an alternative for decision making in the financial stock markets. RNN has also been
applied to other types of financial assets. Ye (2017) focuses on forecasting exchange rate using
gradient descent method or hidden layer in the process learning for recurrent neural networks.
Recurrence in neurons causes a speed up the weights update as well as convergence. This
confirms the reliability and stability of neural networks.
There are dierent types of recurrent neural networks. The Long Short-Term Recurrent
Neural Networks are the most powerful time dynamic neural network (Staudemeyer & Roth-
stein Morris, 2019). This type of network has been applied in many areas. Among others, in
the text translation (Datta, David, Mittal, & Jain, 2020; Nowak, Taspinar, & Scherer, 2017), large
vocabulary speech recognition (Li & Wu, 2015), medicine diagnostic (Choi, Schuetz, Stewart,
& Sun, 2016; Gao, Zhang, Lu, & Wang, 2019), traic control in cities or its environmental im-
pact (Awan, Minerva, & Crespi, 2020). Also for forecasting economics and financial time series
(Siami-Namini, Tavakoli, & Namin, 2018).
In Section 2, the well-known time series models, Arima and Exponential Smoothing, are
described. This is followed by a more in-depth description of Recurrent Neural Networks (RNN)
and the particular Long Short-Term Recurrent Neural Network (LSTM). Section 3 describes the
main results obtained in the work. Finally, Section 4 summarizes the main conclusions.
2 Data and Methods
In this section, the models used in this work are discussed. First, the well-known time series
models, Exponential smoothing and Autoregressive moving average model, are presented in
the summary form. Next, the recurrent neural network model is described in more detail, in
particular, the long-short term memory recurrent neural network model.
2.1 Exponential smoothing model
The exponential smoothing model was proposed at the end of the ‘50s (Brown, 1959; Holt, 2004;
Winters, 1960). In this type of model, past observations are weighted in a way that declines
exponentially the further back in time.
In other words, more recent observations are associated with a greater weight while older
observations have lower weights.
The model can be expressed as follow:
Javier Oliver Muncharaz 139
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
t +1
= α y
+ α (1 α)y
t 1
+ α (1 α)
t 2
+ . . . (1)
α [0, 1]
is the smoothing parameter. Thus, the prediction at instant
t + 1
is a
weighted average of the observations of
. The degree of the weightings decrease is controlled
by the parameter α.
2.2 Autoregressive moving average model
The Autoregressive moving average model (ARMA) was introduced by Box, Jenkins, and Reinsel
(1970). It is one of the classic models that analyses time series, and one of the most used in
financial literature. These models can become stationary by dierencing. Generally, in most
economic and financial time series, a single dierentiation is enough to make the series station-
ary and to be able to apply ARIMA models where the “I” represents the level of dierentiation
(integration) of the series.
Having a time series
represents the time index, the
AR M A(p, q)
model is
expressed as:
= α
t 1
+ α
t 2
+ . . . + α
t p
t 1
t 2
. . . θ
t q
Where α and θ are estimated coeicients and are white noise errors.
AR M A(p, q)
model is built as the combination of two processes. The first is the au-
toregressive process (AR), which tries to predict the variable using a linear combination of past
values of this variable. An autoregressive model of order
, represents the number of lagged
variable. On the other hand, the moving average (MA) part gives a prediction of the variable
from a moving average model on past prediction errors. The order
of this process represents
the number of delays over the prediction errors used in the model.
2.3 Recurrent neural network: LSTM network
Recurrent neural network (RNN) is a network that has backward connections between neurons,
which are generally referred to as global recurrent networks. This type of model presents some
stability problems in the training process, so it requires complex learning algorithms as well
as increasing the training time. Local networks models are global feedforward networks. In
this case, a structure of dynamic models of neurons is designed to build a feedback network, in
which the connections between these neuron models are strictly feedforward as in the case of
Multilayer Perceptron (MLP).
Figure 1 shows an example of the connections between the dierent layers and neurons in a
recurrent neural network. It can be seen how the output obtained in one layer serves as an input
for the neurons of layers located in a previous process. Each recurring unit formed by dierent
neurons computes at each time step an output
which is time dependent on the current
process. In the next time step, the neuron receives a new input vector
and additionally
incorporates the output obtained previously into this vector (
t 1
). The latter is called the
recurrent input. In this way, the neuron computes the output vector from the input vector (
and the recurrent input (
t 1
) using an activation function
. This activation function can be
of the linear, sigmoidal or tanh type, although the last type of function is oen used for time
series problems.
= θ
W × x
, U × y
t 1
Javier Oliver Muncharaz 140
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Figure 1. Recurrent Neural Network representation
Source: Ciaburro and Venkateswaran (2017)
are weight matrix that multiply the input vector and the recurrent input
The simplest recurrent neural network, called "vanilla", presents as recurrent inputs only
a single output obtained in a previous time step. When the net uses the previous outputs as
a new input, the net can remember learned previous data. This process is important for the
learning long short-dependencies.
The importance of inputs and recurrent inputs in the net depends on their corresponding
weight matrix. During the learning process, the net adjusts the weights to improve the pre-
diction, taking into account the calculated error (bacpropagation process). However, while
in a feed forward network the backpropagation process goes back through the hidden layers,
for recurrent neural network it is also necessary to adjust the weights of previous time steps
(time adjusting). In this type of network, if the sequence is long, there may be a problem in
the learning process, since with each prediction the whole way backwards must be covered
again. To avoid this, a split of the dierent sequences is made. In this way, the backpropagation
process should only go backwards the length of the subsequence. But in this case, the neural
network is only able to determine short dependencies. This is the so-called vanishing gradient
problem, in which the further back the sequence is regressed the less important it is in the
current prediction, and therefore cannot adequately capture long term dependencies.
The Long Short-Term Neural Network (LSTM) is a more complex kind of recurrent neural
network as it is able to capture long-term dependencies. This kind of neural network was
proposed by Hochreiter and Schmidhuber (1997) as an evolution of simple RNN. This network
can propagate activations over long periods to process dierent sequences that include long
distance dependencies (Kelleher, 2019). This network solves the vanishing gradient problem. In
this case, the recurrent unit is modified in blocks, which works like a normal recurrent unit, to
which an additional cell and several gates are added. The gates control the flow of information
within the recurrent unit (block). In this way it is determined which information is more revealing
to improve the prediction and which is not at each of the time steps. These gates (
) are defined
Javier Oliver Muncharaz 141
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Type of gate Role
Forget Eliminate neuron
Update Importance of the past
Relevance Drop previous information
Output Which information is used
Table 1. Role Gates
Source: Author’ elaboration
as follow:
τ = σ
W × x
+ U × y
t 1
+ b
are gate specific coeicients and
is the common used sigmoid function
(while in the input activation function use a tanh function). In the LSTMrecurrent neural network,
four gates are used, each with a dierent function. Table 1 summarizes the role function that
one of them has.
The forget gate is used to erase a neuron or not, and therefore, forget the information. On
the other hand, the update gate indicates what is the past to be taken into account now. The
relevance gate defines what information from the past is relevant to incorporate as input to
the neuron. Finally, the output gate selects the information that is useful for the neuron in the
actual prediction. Each of these four gates uses dierent weight matrices and are calculated
individually during the learning process. In short, these gates control the flow of information in
each neuron so that it is useful in predicting at each time step.
3 Results
In this work, it is intended to confirm the eiciency of a LSTM Neural Network, as opposed to
some classic models applied to time series. In this case, it is going to be compared with an
Exponential Smooth Time Series model and an ARIMA model. For this purpose, each of them
has been applied to a sample of 284 stocks from the S&P 500 index with daily data from the last
20 years. The sample has been divided into 70% for the estimation and training processes and
30% for its validation.
For the Exponential Smooth Time Series and ARIMA model, the number of dierentiations
needed to obtain stationary time series, which is required in this type of models, has been
taken into account. As with many economic time series (McCabe & Tremayne, 1995), only one
integration was necessary to achieve stationarity.
For the Exponential Smooth Time Series model, the AIC (Akaike) crystals have been used to
select the appropriate delays in each case. In the case of the ARIMA models, Phillips Perron’s
criteria has been used to determine the delays of both the autoregressive part and the moving
In the case of the LSTM Neural Network model, the series has been standardised, both for
training and for testing. There are many works that verify that standardisation improves the
learning process in neural networks such as Lachtermacher and Fuller (1995); Shen, Zhang, Lu,
Xu, and Xiao (2020); Zhang, Patuwo, and Hu (1998).
Javier Oliver Muncharaz 142
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Figure 2. Example LSTM parameters for 3M stock
Source: Author’ elaboration
Figure 2 shows the type of network applied to each of the actions. As already indicated, it is
a recurrent long short-term neural network. In this case, the processes the sequence of vectors
using a LSTM layer of input data. This model presents the dierent layers in a sequential way.
As the model needs to know in the first layer the type of input it should expect, (since in the
rest of layers it is inferred automatically), the number of samples per gradient updates is one.
That is, the number of batch size of the inputs for the layer is one. The dimension of the output
space of this first layer is five. This parameter is subject to tuning. The output layer is full-fully
connected (dense layer), it has been configured with a batch size of one and one unit.
The three models have been estimated for each stock with the corresponding appropriate
delays according to the criteria already indicated. For the evaluation of the eiciency of each
model, the Mean Absolute Error (MAE) has been calculated on the predicted observations.
Figure 3 shows a boxplot with the errors of each model for the 3M action. In the 284 stocks
analysed, two important issues have been observed. Firstly, the Exponential Smooth Time
Series model and the ARIMA model present similar MAE. For example, in the case of 3M the MAE
obtained in the first model was 0.8847, while for the ARIMA model it was 0.8857. It is possible
that by applying other exponential models such as Holt-Winters’ that could relatively improve
the ARIMA model (Maria & Dezsi, 2011). Secondly, even in the case of using other exponential
models that improve the ARIMA model, they are far removed from the results obtained from
MAE for the LSTM model. For example, for 3M the MAE obtained was 0.1823, that is, 79% less
error than the other models.
Table 2 describes the main statistics on the distribution of the MAE obtained in the total
number of actions analysed and for each of the models. On the one hand, it can be seen that
the classic time series models (ETS and ARIMA) present a higher MAE for all the quantiles of
the sample in comparison with the LSTM model, as it was already advanced in the previous
Javier Oliver Muncharaz 143
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Figure 3. MAE comparison model for 3M stock
Source: Author’ elaboration
example. These results are consistent with other studies such as Siami-Namini et al. (2018)
that compare these three models for various stock market indexes such as Nasdaq, Nikkei,
Hang Seng with monthly data. The results suggest that the LSTM model obtains, on average, a
reduction in prediction error of between 84 and 87 percent. Baughman, Haas, Wolski, Foster,
and Chard (2018) compare the ARIMA model with the LSTM for Amazon stock, obtaining an
error reduction of 95%.
However, four stocks have been detected in which the MAE obtained by the LSTM model
is superior to any of the other two models (Table 3). Each of these stocks has been analyzed
in detail to detect if this result is due to some kind of error in the sample. In all four cases,
there are a suicient number of observations (several thousand). Neither have any missing
or anomalous data been detected. Likewise, the quoted prices have been visually contrasted
without apparently detecting any errors. The first two shares, LDOS and IRM, are listed on the
NYSE, while CTSH and CHTR are listed on the NASDAQ. It can therefore be concluded that the
resultsobtained for these four shares are plausible. However, the LSTM model has outperformed
the classical time series models in 98.59% of the sample analysed, so recurrent neural networks
are a good alternative for time series prediction in general, and for stocks and stock indices in
particular. Abdoli (2020) analyses the Tehran Stock Exchange confirming the results obtained in
the present work, where the LSTM outperforms ARIMA model, in terms of error of accuracy.
4 Conclusions
In this work, the eiciency of the Long short-termn recurrent neural network has been analysed
in comparison with other time series models. The main conclusion that can be drawn is that
there is a large reduction in the prediction error of more than 85%, which is in line with previous
Javier Oliver Muncharaz 144
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Min. 0.0626 0.1441 0.0009
1st Qu. 0.3842 0.3866 0.0565
Median 0.5678 0.5766 0.1289
Mean 0.8177 0.8320 0.2199
3rd Qu. 0.8374 0.8397 0.2708
Max. 9.6813 9.7285 3.1888
Sd. 1.0555 1.0693 0.3000
Table 2. Descriptive Statistics
Source: Author’ elaboration
LDOS 0.6080 0.6118 0.9766
IRM 0.2709 0.2701 0.5742
CTSH 0.3843 0.3853 0.9812
CHTR 2.6014 2.6120 3.1888
Table 3. Descriptive Statistics
Source: Author’ elaboration
results from other studies on other financial assets. Recurrent neural networks in general,
and the LSTM in particular, may be an alternative to consider in the creation of stock price
prediction models. However, to confirm these results, this analysis should be extended to other
aspects such as the application of a larger number of fully connected intermediate layers or the
application of tuning of other network parameters.
On the other hand, other authors have proposed other types of neural networks that seem to
oer very eicient alternatives, as well. In M, E.A., Menon, and K.P. (2018) the authors compare
several linear time series models (ARIMA) with non-linear models such as ARCH, GARCH and
Neural Networks. In this case, they apply two types of recurrent neural networks, one LSTM
model and the other Convolutional Neural Network. This network is applied to five stocks of
the National Stock Exchange (NSE) of India. The results suggest that the Convolutional Neural
Network outperforming the other models, even against the LSTM model. In the same line, the
works of Y. Chen, Wei, and Huang (2018)applying a Convolutional model to the prediction of the
stock market in Mainland China incorporating related corporations’ information to create more
accuracy in predictions are presented. In addition, other works propose the use of a hybrid
model between the Convolutional Neural Network and the recurrent neuronal network LSTM
(Kim & Kim, 2019).
Abdoli, G. (2020). Comparing the prediction accuracy of LSTM and ARIMA mod-
els for time-series with permanent fluctuation.
SSRN Electronic Journal
. doi:
Javier Oliver Muncharaz 145
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Ahn, W., Lee, H. S., Ryou, H., & Oh, K. J. (2020). Asset allocation model for a robo-advisor using
the financial market instability index and genetic algorithms.
(3), 849.
Arribas, I., Espinós-Vañó, M. D., García, F., & Oliver, J. (2019). Defining socially responsible
companies according to retail investors’ preferences.
Entrepreneurship and Sustainability
Issues, 7(2), 1641–1653. doi:
Awan, F. M., Minerva, R., & Crespi, N. (2020). Improving road traic forecasting using air pollution
and atmospheric data: Experiments based on LSTM recurrent neural networks.
20(13), 3749. doi:
Barkoulas, J. T., & Baum, C. F. (1996). Long-term dependence in stock returns.
Letters, 53(3), 253–259. doi:
Baughman, M., Haas, C., Wolski, R., Foster, I., & Chard, K. (2018). Predicting amazon spot prices
with LSTM networks. In
Proceedings of the 9th workshop on scientific cloud computing.
ACM. doi:
Box, G. E., Jenkins, G. M., & Reinsel, G. (1970).
Time series analysis: forecasting and control
holden-day san francisco. Holden Day.
Brown, R. G. (1959). Statistical forecasting for inventory control. McGraw/Hill.
Chen, W., Zhang, H., Mehlawat, M.K., &Jia, L. (2021). Mean–varianceportfolio optimization using
machine learning-based stock price prediction.
Applied So Computing
, 106943. doi:
Chen, Y., Wei, Z., & Huang, X. (2018). Incorporating corporation relationship via graph
convolutional neural networks for stock price prediction. In
Proceedings of the 27th
ACM international conference on information and knowledge management.
ACM. doi:
Choi, E., Schuetz, A., Stewart, W. F., & Sun, J. (2016). Using recurrent neural network models
for early detection of heart failure onset.
Journal of the American Medical Informatics
Association, 24(2), 361–370. doi:
Ciaburro, G., & Venkateswaran, B. (2017).
Neural networks with r: Smart models using cnn, rnn,
deep learning, and artificial intelligence principles. Packt Publishing Ltd.
da Silva, I. N., Spatti, D. H., Flauzino, R. A., Liboni, L. H. B., & dos Reis Alves, S. F. (2016). Forecast of
stock market trends using recurrent networks. In
Artificial neural networks
(pp. 221–227).
Springer International Publishing. doi:
Datta, D., David, P. E., Mittal, D., & Jain, A. (2020). Neural machine translation using recurrent
neural network.
International Journal of Engineering and Advanced Technology
Espinós-Vañó, M. D., García, F., & Oliver, J. (2018). The ethical index FTSE4good IBEX as an
alternative for passive portfolio strategies in spain.
Finance, Markets and Valuation
85–93. doi:
Gao, J., Zhang, H., Lu, P., & Wang, Z. (2019). An eective LSTM recurrent network to detect
arrhythmia on imbalanced ECG dataset.
Journal of Healthcare Engineering
, 1–10.
García, F., González-Bueno, J., Oliver, J., & Tamoši
e, R. (2019). A credibilistic mean-
semivariance-per portfolio selection model for latin america.
Journal of Business Eco-
nomics and Management
(2), 225–243. doi:
García, F., González-Bueno, J. A., & Oliver, J. (2015). Mean-variance investment strategy applied
Javier Oliver Muncharaz 146
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
in emerging financial markets: Evidence from the colombian stock market.
Economics, 9(1), 22–29. doi:
García, F., Guijarro, F., & Oliver, J. (2018). Index tracking optimization with cardinality constraint:
a performance comparison of genetic algorithms and tabu search heuristics.
Computing and Applications
(8), 2625–2641. doi:
García, F., Guijarro, F., Oliver, J., & Tamoši
e, R. (2018). Hybrid fuzzy neural network to pre-
dict price direction in the german dax-30 index.
Technological and Economic Development
of Economy, 24(6), 2161–2178. doi:
Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory.
Neural Computation
1735–1780. doi:
Holt, C. C. (2004). Forecasting seasonals and trends by exponentially weighted
moving averages.
International Journal of Forecasting
(1), 5–10. doi:
Hopfield, J. J., & Tank, D. W. (1985). “neural” computation of decisions in optimization problems.
Biological cybernetics, 52(3), 141–152.
Kelleher, J. D. (2019). Deep learning. Mit Press.
Kim, T., & Kim, H. Y. (2019). Forecasting stock prices with a feature fusion LSTM-CNN model
using dierent representations of the same data.
(2), e0212320. doi:
Lachtermacher, G., & Fuller, J. D. (1995). Back propagation in time-series forecasting.
of Forecasting, 14(4), 381–393. doi:
Li, X., & Wu, X. (2015). Constructing long short-term memory based deep recurrent neural
networks for large vocabulary speech recognition. In
2015 ieee international conference
on acoustics, speech and signal processing (icassp) (pp. 4520–4524).
M, H., E.A., G., Menon, V. K., & K.P., S. (2018). NSE stock market prediction us-
ing deep-learning models.
Procedia Computer Science
, 1351–1362. doi:
Maria, F. C., & Dezsi, E. (2011). Exchange-rates forecasting: Exponential smoothing techniques
and arima models. Annals of Faculty of Economics, 1(1), 499–508.
McCabe, B. P., & Tremayne, A. R. (1995). Testing a time series for dierence stationarity.
Annals of Statistics, 1015–1028.
Moghaddam, A. H., Moghaddam, M. H., & Esfandyari, M. (2016). Stock market index prediction
using artificial neural network.
Journal of Economics, Finance and Administrative Science
21(41), 89–93. doi:
Nowak, J., Taspinar, A., & Scherer, R. (2017). LSTM recurrent neural networks for short text
and sentiment classification. In
Artificial intelligence and so computing
(pp. 553–562).
Springer International Publishing. doi:
Qiu, M., & Song, Y. (2016). Predicting the direction of stock market index movement us-
ing an optimized artificial neural network model.
(5), e0155133. doi:
Rather, A. M., Agarwal, A., & Sastry, V. (2015). Recurrent neural network and a hybrid model
for prediction of stock returns.
Expert Systems with Applications
(6), 3234–3241. doi:
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-
propagating errors. nature, 323(6088), 533–536.
Javier Oliver Muncharaz 147
Finance, Markets and Valuation Vol. 6, Num. 2 (Julio-Diciembre 2020), 137–148
Saad, E., Prokhorov, D., & Wunsch, D. (1998). Comparative study of stock trend prediction using
time delay, recurrent and probabilistic neural networks.
IEEE Transactions on Neural
Networks, 9(6), 1456–1470. doi:
Shen, Z., Zhang, Y., Lu, J., Xu, J., & Xiao, G. (2020). A novel time series
forecasting model with deep learning.
, 302–313. doi:
Siami-Namini, S., Tavakoli, N., & Namin, A. S. (2018). A comparison of arima and lstm in
forecasting time series. In
2018 17th ieee international conference on machine learning
and applications (icmla) (pp. 1394–1401).
Staudemeyer, R. C., & Rothstein Morris, E. (2019). Understanding lstm–a tutorial into long
short-term memory recurrent neural networks. arXiv, arXiv–1909.
Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages. Manage-
ment Science, 6(3), 324–342. doi:
Ye, Y. (2017). Study on exchange rate forecasting using recurrent neural networks.
ternational Journal of Economics, Finance and Management Sciences
(6), 300. doi:
Yoshihara, A., Fujikawa, K., Seki, K., & Uehara, K. (2014). Predicting stock market trends
by recurrent deep neural networks. In
Pacific rim international conference on artificial
intelligence (pp. 759–769).
Zhang, G., Patuwo, B. E., & Hu, M. Y. (1998). Forecasting with artificial neural networks:.
International Journal of Forecasting
(1), 35–62. doi:
Javier Oliver Muncharaz 148