=Paper=
{{Paper
|id=Vol-3682/Paper11
|storemode=property
|title=CGM: A hybrid model for forecasting future stock price
|pdfUrl=https://ceur-ws.org/Vol-3682/Paper11.pdf
|volume=Vol-3682
|authors=Ningyao Ningshen,Vinita Jindal,Punam Bedi
|dblpUrl=https://dblp.org/rec/conf/sci2/NingshenJB24
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==CGM: A hybrid model for forecasting future stock price==
https://ceur-ws.org/Vol-3682/Paper11.pdf
CGM: A hybrid model for forecasting future stock price
Ningyao Ningshen1, *, Vinita Jindal2 and Punam Bedi1
1 Department of Computer Science, University of Delhi, New Delhi, India, 110007
2 Department of Computer Science, Keshav Mahavidyalaya, University of Delhi, New Delhi, India, 110034
Abstract
In finance, Forecasting Stock Price (FSP) poses a significant challenge. However,
the swift progress enabled by Artificial Intelligence (AI) techniques,
particularly Deep Neural Network (DNN) has propelled the advancements in
this sector. Consequently, researchers have investigated the application of
different DNN techniques. Despite these efforts, existing models are often
shallow and prone to overfitting due to the model's complexity. Consequently,
there is still room for improvement in achieving accurate forecasts of the future
closing price. Therefore, to advance FSP, a novel hybrid model named CGM is
proposed, which is developed using a combination of Convolution, Gated
Recurrent Unit (GRU), and Multi-Layer Perceptron (MLP). Thereafter, the CGM
model is trained using technical features, Intrinsic Mode Function (IMF)
decomposed using Empirical Mode Function (EMD), and a combination of both
to exhaustively explore the ability of the CGM model, thus producing three
distinct models, namely TF-CGM, IMF-CGM, and TF-IMF-CGM models.
Furthermore, to automatically tailor the hyperparameters of the
aforementioned models, Neural Architectural Search (NAS) is employed to
automatically fine-tune the hyperparameters of the models. During the
experiment, the aforementioned models are evaluated using Root Mean Square
Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage
Error (MAPE) evaluation metrics using stock indices listed in the New York
Stock Exchange (NYSE) and National Stock Exchange (NSE). From the
experimental results, it was observed that technical features exert a more
significant influence, which leads to the TF-CGM model outperforming the IMF-
CGM and TF-IMF-CGM models. Moreover, the proposed models provided better
performance when compared with existing models present in the literature.
Keywords
Finance, Artificial Intelligence, Machine Learning, Deep Neural Network, Gated Recurrent Unit,
Multi-Layer Perceptron1
Symposium on Computing & Intelligent Systems (SCI), May 10, 2024, New Delhi, INDIA
∗ Corresponding author.
† These authors contributed equally.
nningshen@cs.du.ac.in (N. Ningshen); vjindal@keshav.du.ac.in (V. Jindal); pbedi@cs.du.ac.in (P. Bedi)
0009-0003-8909-8648 (N. Ningshen); 0000-0002-0481-4840 (V. Jindal); 0000-0002-6007-7961 (P. Bedi)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
1. Introduction
Predicting future stock prices and market indices is crucial for investors and traders
seeking positive returns on their investments. However, it remains a challenge due to the
complex dynamics influenced by economic, emotional, and political factors, as suggested by
the Efficient Market Hypothesis (EMH). Despite this, efforts have been made to develop
strategies for successful price prediction [1]. Traditionally, Forecasting Stock Price (FSP)
involves examining historical price movement and trading volumes together with a
comprehensive assessment of a company’s financial health to ascertain its intrinsic value
and potential for future growth. However, such methods presume the presence of
exploitable trends in historical data for forecasting future prices. Therefore, an alternative
method such as statistical models like Auto-Regressive Integrated Moving Average (ARIMA)
and Seasonal ARIMA (SARIMA) are commonly utilized for future price forecasting [2], [3],
[4]. Nevertheless, the linearity inherent in these statistical models limits their ability to
capture the complex dynamics exhibited by historical market data. Consequently, various
researchers have explored the usage of Deep Neural Network (DNN) in FSP [1], [5], [6], [7],
[8]. However, due to the shallow nature of the existing models, they are susceptible to
overfitting. Therefore, this research paper aims to address this limitation by proposing a
novel hybrid model named CGM, which employs a combination of Convolution, Gated
Recurrent Unit (GRU), and Multi-Layer (MLP) Perceptron techniques.
A convolutional layer is a building block of a Convolutional Neural Network (CNN) [9],
which is widely used in image analysis. It involves a convolution operation, wherein filters
slide across the input data, performing an element-wise multiplication between the filter
and the input to extract localized spatial information. Meanwhile, GRU, introduced by [10],
is a category of Recurrent Neural Networks (RNN), which is specifically designed to address
the challenges of RNN in capturing long-range dependencies. Furthermore, MLP, a type of
fully connected feedforward ANN is also utilized in the development of the CGM model.
During the experiment, the hybrid CGM model is trained using three different types of
inputs i.e., Technical Features (TFs), Intrinsic Mode Functions (IMFs), and a combination of
both features, thereby producing three unique variants of the CGM model, namely TF-CGM,
IMF-CGM, and TF-IMF-CGM models. Furthermore, the Neural Architectural Search (NAS)
algorithm [11], which is a subfield in Machine Learning (ML) for streamlining the ML
pipeline is introduced to facilitate automatic hyperparameter tuning in the TF-CGM, IMF-
CGM, and TF-IMF-CGM models.
The manuscript is divided into six sections. Section 2 presents the summary of the
existing literature centered on stock price prediction using DNN techniques. Sections 3 and
4 delve into the proposed work and its experimental study, which is followed by presenting
the results and discussion of the experiment in Section 5. Finally, Section 6 presents the
conclusion of the research work.
2. Literature Review
In the last decade, researchers have increasingly turned to DNN for stock price
prediction, leveraging their capability to capture non-linear dependencies in financial time
series data. In the research work conducted by Selvamuthu et al., (2019), three learning
techniques, namely Levenberg-Marquardt (LM), Scaled Conjugate Gradient (SCG), and
Bayesian Regularization (BR) were explored. Their experimental results, assessed using
both tick data and 15-minute data revealed that SCG exhibited superior performance in
comparison to LM and BR. However, the authors concluded that incorporating LSTM and
integrating sentiment analysis could potentially yield better results. In a comparable
investigation carried out by Cao et al., (2019), time-series financial data underwent
decomposition into IMFs through the application of both Empirical Mode Decomposition
(EMD) and Complete Ensemble Mode Decomposition with Adaptive Noise (CEEMDAN)
techniques, and its influence was assessed using a two-layered LSTM model. They observed
that two-layered LSTM outperformed one-layered LSTM, MLP, and Support Vector Machine
(SVM). Moreover, Chen et al., (2019) explored the application of the attention mechanism
in LSTM for stock market prediction. Their experiment was verified using the SSE stock
index and found that LSTM with an attention mechanism has more potential, thereby
achieving better results compared to standalone LSTM. In the subsequent research work
conducted by Shen & Shafiq, (2020), the effectiveness of LSTM was investigated in short-
term trend forecasting for market prices. Their approach encompassed feature expansion
steps using min-max scaling, polarization, and computing percentage fluctuation. They
contended that the superiority of their model over others stems from the comprehensive
feature engineering employed in their methodology. Taking a different approach, Yang et
al., (2020) leveraged three-dimensional CNN to extract features from stock data meanwhile,
LSTM was used for prediction. However, they opted to exclude the pooling layers in their
experiment to prevent potential information loss. Their findings underscored the
significant role of ranking stock indices in enhancing the overall performance of their
models.
In a more recent study conducted by Ji et al., (2021), an LSTM model was proposed for
stock price prediction. Their study involved decomposing the stock data into deterministic
signals through wavelet transform techniques. Additionally, sentiment analysis was
incorporated by utilizing text data acquired from social media. Their experimentation
demonstrated success when compared to traditional models. To emphasize the significance
of utilizing DNN in forecasting future metal prices in the metal industry, Lin et al., (2022)
proposed a novel model that is based on Modified Ensemble Empirical Mode Decomposition
(MEEMD) and LSTM. They pointed out that MEEMD demonstrated a better decomposition
effect than EMD. In [19], a novel architecture named FDGRU-transformer (Frequency
Decomposition induced Gate Recurrent Unit Transformer) was proposed to tackle the stock
price prediction problem. Their method involved decomposing stock data into IMFs using
the EMD technique. Furthermore, a GRU, LSTM, and multi-head attention were utilized to
extract temporal information. Their model’s comparison with existing state-of-the-art
models indicated better results. Moreover, as a consequence of ANN’s popularity in FSP,
Seabe et al., (2023) explored the capability of LSTM, GRU, and bi-directional LSTM in
forecasting the price of Bitcoin, Ethereum, and Litecoin. Their model’s evaluation illustrated
that bi-directional LSTM possesses the highest capability in predicting the prices of the
cryptocurrencies.
Despite the success in the application of DNN in FSP, the existing models are often
characterized by limited depth, potentially leading to overfitting. Therefore, to address this
limitation and enhance the prediction accuracy, this research work introduces a novel
hybrid model, named CGM by integrating Convolution, GRU, and MLP techniques.
Furthermore, to achieve a balance between model prediction performance and
representativeness in architectural configurations, the NAS algorithm is employed to
automatically optimize hyperparameters, eliminating the need for manual hyperparameter
tuning. A detailed description of the proposed hybrid CGM model is presented in the
following section.
3. Proposed CGM model
Conventional methods such as time series analysis and statistical approaches have
established the groundwork for comprehending market dynamics. However, due to the
subjective and non-linear characteristics inherent in traditional approaches, contemporary
methodologies like DNN techniques offer more promising alternatives for FSP. Nonetheless,
existing DNN models are often shallow, and susceptible to overfitting. Therefore, this
research work aims to contribute to the ongoing discourse by proposing a novel hybrid
model, named CGM, which stands for Convolution, GRU, and MLP respectively. The
proposed hybrid CGM model (given in Figure 1) comprises an Input block, a Conditional
block, and an Output block. The components are discussed below.
Figure 1. Visual representation of the hybrid CGM model
3.1. Input block
The Input block of the CGM model incorporates Convolution, GRU, and MLP modules.
The Convolution module consists of four Convolutional layers. The initial layer establishes
a connection with the input layer. Subsequently, the output is concurrently fed into three
parallel Convolutional layers, capturing various aspects and representations of the input
data. In tandem with the Convolution module, the Input block also integrates a GRU module
to learn feature dependencies over long ranges. Similar to the Convolution module, the first
GRU layer establishes a connection with the input layer. The resulting output is then
directed to two subsequent GRU layers for further processing, and their outputs are
aggregated before being forwarded to subsequent layers. Additionally, to augment feature
extraction capability, an MLP module is also employed, comprising three Dense layers.
Analogous to the aforementioned modules, the initial Dense layer receives input from the
input layer and its output is concurrently transmitted to two Dense layers. The resulting
outputs are amalgamated and forwarded for subsequent processing. The visual
representation of the Convolution, GRU, and MLP modules of the Input block are given in
Figure 2 (a), (b), and (c) respectively.
Figure 2. (a) Convolution, (b) GRU, and (c) MLP modules.
3.2. Conditional and Output block
In the Conditional block, three sets of Dropout and Normalization layers are arranged
parallelly to improve training stability, prevent overfitting, and further enhance the overall
performance of the model. The input of the Conditional block is derived from the
Convolution, GRU, and MLP modules of the preceding block. Each of these modules feeds
independently into the corresponding Dropout and Normalization layers within the
Conditional block. The visual representation of the Conditional block is given in Figure 3 (a).
After the Conditional block, the outputs are forwarded to the Output block. The Output
block consists of Concatenation, Bi-directional GRU, and Dense Layers. The Concatenation
layer concatenates the input received from the Conditional block to create a unified feature
yielding a more comprehensive feature representation of the input. The concatenation steps
follow the procedure given in Equation 1.
𝑔(𝑛1 , 𝑛2 , 𝑛3 ) 𝑖𝑓 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑏𝑙𝑜𝑐𝑘 = 𝑇𝑟𝑢𝑒
𝑥𝑐𝑜𝑛𝑐𝑎𝑡 = { (1)
𝑔(𝑐1 , 𝑐2 , 𝑐3 ) 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where g is the concatenation operation, 𝑛1 , 𝑛2 , 𝑛3 are the outputs from conditional block
and 𝑐1 , 𝑐2 , 𝑐3 are outputs produced by Convolution, GRU, and MLP modules. The visual
representation of the Output block is given in Figure 3 (b).
Following the concatenation step, the combined output is passed through a bidirectional
GRU layer to handle input from both forward and backward directions. This enables the
model to grasp both past and future context, facilitating the model to capture bi-directional
dependencies within the data. Ultimately, the resulting output is directed to the final Dense
layer with a sigmoid function for predicting the future stock price.
Figure 3. (a) Conditional block and (b) Output block
Throughout the experiment, three models undergo fine-tuning and training using TFs,
IMFs, and combinations of both TFs and IMFs. This process leads to the development of
three distinct CGM models: TF-CGM, IMF-CGM, and TF-IMF-CGM, where TFs are fed as input
to TF-CGM, IMFs into IMF-CGM, and TF+IMFs into TF-IMF-CGM models. Henceforth, we will
refer to these models individually as TF-CGM, IMF-CGM, and TF-IMF-CGM. Furthermore, to
streamline the experimentation process and eliminate manual hyperparameter tuning for
the aforementioned models, the NAS algorithm is employed. This algorithm automatically
determines hyperparameters such as learning rate, activation function, hidden units,
number of filters, and the decision to include or exclude a conditional block during training.
The detailed results of the conducted experiment are discussed in the following section.
4. Experimentation
This section provides an in-depth exploration of the experiments carried out during the
research study. The primary goal of the research is to develop a hybrid model that is
expressive enough (i.e., a representable number of trainable parameters) as well as improve
the performance of predicting future stock prices, thus striking a balance between
complexity and performance.
4.1. Data collection and preprocessing
In the course of the study’s experimentation, daily OHLCV of four stock indices listed in
the New York Stock Exchange (NYSE) and four stock indices listed in the NSE are collected
from Yahoo Finance for training and testing.
Furthermore, during the data preparation, NaN (not a number) values are dropped from
the dataset. Subsequently, lag features with a window size of 5 were constructed from the
independent features. Additionally, the stock data was decomposed into IMFs using the
EMD technique as described in [21]. Subsequently, the time-series data is reorganized to
embed temporal information into the dataset. Naturally, 𝑥𝑡,𝑓 ∈ 𝑋 denotes a singular input,
where 𝑥𝑡,𝑓 represents data at time t with features f. However, during the experiment of this
research work, the input sample 𝑥𝑖 and label 𝑦𝑖 is reconfigured as 𝑥𝑖 =
{𝑥𝑡+𝑖 , 𝑥𝑡+𝑖+1 , … , 𝑥𝑡+𝑖+𝑛 } and 𝑦𝑖 = {𝑦𝑡+𝑖+𝑛+1 }, where the window size n is equal 10.
Moreover, each sample is normalized using a Min-Max Scaler [22]. Following the data
preprocessing, the data are split into training, validation, and testing subsets in a ratio of
7:2:1.
4.2. Experimental configuration and evaluation metrics
During the experimentation, the TF-CGM, IMF-CGM, and TF-IMF-CGM models were
experimented on a Metal Performance Shader (MPS) device. Furthermore, throughout the
experiment, Python v3.11 was used as a primary language, and TensorFlow v2.15 as the ML
framework. Nonetheless, different programming languages and frameworks could be used
for the experiment.
In the initial step of the experiment, the NAS algorithm was used to optimize the
hyperparameters of the aforementioned models independently. The NAS algorithm utilizes
a RandomSearch technique to determine the value of the hyperparameters. The process
involved conducting 10 trials, each comprising four runs to optimize the loss function.
Subsequently, the optimized TF-CGM, IMF-CGM, and TF-IMF-CGM were trained using TFs,
IMFs, and a combination of TFs and IMFs for forecasting the future close price of daily stock
data. The models were trained for 250 epochs with a batch size of 32. Moreover, an early
stopping mechanism is employed during training to prevent the models from overfitting
with a patience of 30 epochs i.e., the training stops if there is no sign of improvement for 30
successive epochs. Furthermore, Adam [23] optimizer was utilized to minimize the loss
function associated with the models.
During the experiment, the Mean Square Error (MSE) given in Equation 2 was used as a
loss function to measure the performance of each trial. However, Root Mean Squared Error
(RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) were
used to evaluate the performance of the models during the training and testing phase. The
mathematical formulae for the metrics are given in Equation 3 – 5.
n
1
𝑀𝑆𝐸 = ∑(yi − ŷi )2 (2)
n
i=1
RMSE = √MSE (3)
∑ni=1|yi − ŷi |
MAE = (4)
n
n
1 yi − ŷi
MAPE = ∑ | | (5)
n yi
i=1
5. Results and Discussion
This section presents the results of the hybrid CGM model in predicting the future close
price of daily stock data. As previously stated, three variations of the hybrid CGM model,
namely TF-CGM, IMF-CGM, and TE-IMF -CGM underwent hyperparameters tuning
individually. The results of the NAS algorithm during hyperparameter optimization for the
aforementioned models are given in Table 1.
Table 1. Hyperparameters selected by the NAS algorithm during hyperparameter tuning
Hyperparameters TF-CGM IMF -CGM TF-IMF-CGM
Activation Function gelu gelu gelu
Learning Rate 5.434e-4 1.089e-4 2.598e-4
Dropout Layer True False True
Normalization Layer True False False
GRU units 192 160 128
MLP units 192 160 128
Convolution filter size 160 32 64
Trainable Parameters 1, 587, 493 955, 137 678, 849
From the results presented in Table 1, it is evident that the model favors gelu as the
activation function compared to other activation functions. Furthermore, the
hyperparameter tuning performed by the NAS algorithm consistently opts for a low
learning rate. However, the determination to include or exclude the conditional block is
contingent on the variant of the model. Subsequently, the models were evaluated on NYSE
and NSE stock data using RMSE, MAE, and MAPE evaluation metrics. The results of TF-CGM,
IMF-CGM, and TE-IMF-CGM on the test set are given in Table 2 and 3.
The analysis of Table 2 and 3 leads to the conclusion that TF-CGM exhibited superior
performance when compared to IMF-CGM and TF-IMF-CGM. Additionally, the Linear
Regression Analysis (LRA) on NYSE and NSE shown in Figure 4 further substantiates the
supremacy of TF-CGM over IMF-CGM and TF-IMF-CGM in forecasting the future closing
prices of daily stock data. Furthermore, to bolster the claim of the proposed model's
superiority, the performance of the models was compared with models documented in the
existing literature given in Table 3.
Table 2. Evaluation results of TF-CGM, IMF-CGM, and TF-IMF-CGM models on NYSE stock
indices.
Ticker Model RMSE MAE MAPE
TF-CGM 3.47 2.58 0.037
AAPL IMF-CGM 4.89 3.08 0.030
TF-IMF-CGM 2.79 2.79 0.030
TF-CGM 2.24 1.63 0.022
ABT IMF-CGM 3.45 2.45 0.029
TF-IMF-CGM 2.97 2.13 0.026
TF-CGM 6.20 4.73 0.030
MSFT IMF-CGM 9.75 6.34 0.030
TF-IMF-CGM 8.29 5.42 0.026
TF-CGM 3.82 2.41 0.063
AMD IMF-CGM 2.84 1.53 0.041
TF-IMF-CGM 4.09 2.38 0.060
TF-CGM 3.93 2.83 0.038
Mean IMF-CGM 5.23 3.35 0.032
TF-IMF-CGM 4.53 3.18 0.035
Table 3. Evaluation results of TF-CGM, IMF-CGM, and TF-IMF-CGM models on NSE stock
indices.
Ticker Model RMS MAE MAPE
E
RELIANCE TF-CGM 65.34 49.24 0.027
IMF-CGM 106.01 82.54 0.038
TF-IMF-CGM 91.56 72.12 0.037
TATACONSUM TF-CGM 17.57 13.056 0.028
IMF-CGM 31.77 22.93 0.036
TF-IMF-CGM 22.33 16.41 0.031
SBIN TF-CGM 14.35 10.87 0.032
IMF-CGM 19.61 13.46 0.031
TF-IMF-CGM 17.58 13.40 0.036
CIPLA TF-CGM 24.19 16.84 0.022
IMF-CGM 36.49 25.16 0.028
TF-IMF-CGM 35.99 27.94 0.035
TF-CGM 30.36 22.50 0.027
Mean IMF-CGM 48.47 36.02 0.033
TF-IMF-CGM 41.86 32.46 0.034
Figure 4. Linear Regression Analysis of TF-CGM, IMF-CGM, and TF-IMF-CGM on NYSE and
NSE stock indices.
The analysis of Table 2 and 3 leads to the conclusion that TF-CGM exhibited superior
performance when compared to IMF-CGM and TF-IMF-CGM. Additionally, the Linear
Regression Analysis (LRA) on NYSE and NSE shown in Figure 4 further substantiates the
supremacy of TF-CGM over IMF-CGM and TF-IMF-CGM in forecasting the future closing
prices of daily stock data. Furthermore, to bolster the claim of the proposed model's
superiority, the performance of the models was compared with models documented in the
existing literature given in Table 4.
Table 4. Performance comparison of the proposed hybrid model with the models present in
the existing literature. The given scores for TF-CGM, IMF-CGM, and TF-IMF-CGM are the
mean of the scores obtained in the NYSE and NSE stock indices given in Table 2 and 3.
Model RMSE MAE MAPE
[12] (SCG+ANN) - - 99.908
[14] (EMD+LSTM+ATTENTION) 26.10 16.39 0.66
[24] (Convolution+LSTM) 386.47 - -
[25] (LASSO-GRU) 27.45 19.14 -
[20] (bi-LSTM) 373.77 - 0.067
[26] (GRU) 0.084 22.94 0.259
TF-CGM (proposed) 17.14 12.66 0.032
IMF-CGM (proposed) 26.85 19.68 0.032
TF-IMF-CGM (proposed) 23.19 17.82 0.033
From the results presented in Table 2 and 3, it can be concluded that TF-CGM
outperforms IMF-CGM and TF-IMF-CGM, emphasizing the significant impact of technical
factors on the model. Additionally, the models display reduced efficacy when applied to NSE
data, as indicated by higher RMSE and MAE values, signifying a relatively larger margin of
error. However, the models exhibit relatively similar MAPE values on NSE data, which
indicates comparatively similar relative size errors in accuracy. The disparity in the scores
of TF-CGM, IMF-CGM, and TF-IMF-CGM on NYSE and NSE data implies variations in the
factors influencing the NYSE and NSE markets. Therefore, future research could involve
exploring market dynamics and examining the variables that affect the performance of the
models. Moreover, sentiment analysis could also be integrated to further enhance the
predictive capability of the models.
6. Conclusion
Forecasting future stock prices poses a significant challenge in the financial sector, and
addressing this challenge has been an active area of research. Hence, various researchers
have contributed to this field by developing models using modern DNN techniques.
However, existing models tend to be shallow and susceptible to overfitting. To address this
challenge, this research paper proposes a hybrid CGM model that incorporates Convolution,
GRU, and MLP techniques.
Moreover, to comprehensively assess the effectiveness hybrid CGM model, three
different inputs – TFs, IMFs, and a combination of both – were used to train the CGM model,
resulting in three distinct models, namely TF-CGM, IMF-CGM, and TF-IMF-CGM models.
Furthermore, to tackle the challenges associated with tailoring the hyperparameters of the
models, the NAS algorithm was employed to automatically optimize the hyperparameters.
These models were then trained and tested using four stock indices listed in the NYSE and
four stock indices listed in the NSE. Thereafter, the performance of the models was
evaluated using RMSE, MAE, and MAPE metrics. From the experiment, it was found that TF-
CGM outperformed the IMF-CGM and TF-IMF-CGM models by scoring 3.93, 2.83, and 0.038
on NYSE data, and 30.36, 22.50, and 0.027 on NSE data respectively for the aforementioned
evaluation metrics. Moreover, the proposed models were compared with existing models,
the proposed models demonstrated superior performance.
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