A Hybrid AI Framework for Enhanced Stock Movement Prediction: Integrating ARIMA, RNN, and LightGBM Models

Abstract

Forecasting stock market movements is a critical yet challenging endeavor due to the inherent nonlinearity, chaotic behavior, and dynamic nature of financial markets. This study proposes the Autoregressive Integrated Moving Average Ensemble Recurrent Light Gradient Boosting Machine (AR-ERLM), an innovative model designed to enhance the precision and reliability of stock movement predictions. The AR-ERLM integrates ARIMA for identifying linear dependencies, RNN for capturing temporal dynamics, and LightGBM for managing large-scale datasets and non-linear relationships. Using datasets from Netflix, Amazon, and Meta platforms, the model incorporates technical indicators and Google Trends data to construct a comprehensive feature space. Experimental results reveal that the AR-ERLM outperforms benchmark models such as GA-XGBoost, Conv-LSTM, and ANN. For the Netflix dataset, the AR-ERLM achieved an RMSE of 2.35, MSE of 5.54, and MAE of 1.58, surpassing other models in minimizing prediction errors. Moreover, the model demonstrates robust adaptability to real-time data and consistently superior performance across multiple metrics. The findings emphasize AR-ERLM’s potential to enhance predictive accuracy, mitigating overfitting and reducing computational overhead. These implications are crucial for financial institutions and investors seeking reliable tools for risk assessment and decision-making. The study sets the foundation for integrating advanced AI models into financial forecasting, encouraging future exploration of hybrid optimization techniques to further refine predictive capabilities.

Full text

Academic Editors: Hang Xiong,
Quan Bai, Peng Lv and Zhou He
Received: 19 December 2024
Revised: 21 February 2025
Accepted: 23 February 2025
Published: 26 February 2025
Citation: Alarbi, A.; Khalifa, W.;
Alzubi, A. A Hybrid AI Framework
for Enhanced Stock Movement
Prediction: Integrating ARIMA, RNN,
and LightGBM Models. Systems 2025,
13, 162. https://doi.org/10.3390/
systems13030162
Copyright: © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/
licenses/by/4.0/).
Article
A Hybrid AI Framework for Enhanced Stock Movement
Prediction: Integrating ARIMA, RNN, and LightGBM Models
Adel Alarbi, Wagdi Khalifa and Ahmad Alzubi *
Institute of Graduate Research and Studies, University of Mediterranean Karpasia, 33010 Mersin, Turkey;
210634357@std.akun.edu.tr (A.A.); wagdi.kalifa@akun.edu.tr (W.K.)
*Correspondence: ahmad.alzaubi@akun.edu.tr
Abstract: Forecasting stock market movements is a critical yet challenging endeavor due
to the inherent nonlinearity, chaotic behavior, and dynamic nature of financial markets.
This study proposes the Autoregressive Integrated Moving Average Ensemble Recurrent
Light Gradient Boosting Machine (AR-ERLM), an innovative model designed to enhance
the precision and reliability of stock movement predictions. The AR-ERLM integrates
ARIMA for identifying linear dependencies, RNN for capturing temporal dynamics, and
LightGBM for managing large-scale datasets and non-linear relationships. Using datasets
from Netflix, Amazon, and Meta platforms, the model incorporates technical indicators and
Google Trends data to construct a comprehensive feature space. Experimental results reveal
that the AR-ERLM outperforms benchmark models such as GA-XGBoost, Conv-LSTM,
and ANN. For the Netflix dataset, the AR-ERLM achieved an RMSE of 2.35, MSE of 5.54,
and MAE of 1.58, surpassing other models in minimizing prediction errors. Moreover,
the model demonstrates robust adaptability to real-time data and consistently superior
performance across multiple metrics. The findings emphasize AR-ERLM’s potential to
enhance predictive accuracy, mitigating overfitting and reducing computational overhead.
These implications are crucial for financial institutions and investors seeking reliable tools
for risk assessment and decision-making. The study sets the foundation for integrating
advanced AI models into financial forecasting, encouraging future exploration of hybrid
optimization techniques to further refine predictive capabilities.
Keywords: stock market forecasting; hybrid AI models; ARIMA-RNN-LightGBM ensemble;
technical indicators analysis; financial time series prediction
1. Introduction
In recent years, stock trading has attained massive growth because of the higher short-
term returns, inflation protection, and secure long-term benefits over other investment
options. With accurate forecasting, an individual can maximize profit by purchasing
stocks that are expected to rise in the future and selling the stocks that are possible to
fall. However, stock prices are highly volatile and erratic, making stock movement a
complex dynamic system that can predict prices [
1
]. In addition, stock prices rely on several
factors, including political, global, and economic situations, as well as the mentality of
investors, which form the reason behind the volatility of the stock market [
2
]. Generally,
the two categories of prediction techniques that are commonly used to assist stock market
investments are fundamental and technical analysis [
3
]. When applying the first approach,
the organization’s financial state, personnel, annual reports, balance sheets, income reports,
and other documents are all taken into consideration. Technical analysis, also known as
Systems 2025,13, 162 https://doi.org/10.3390/systems13030162

Systems 2025,13, 162 2 of 28
charting, conversely, uses historical data to identify patterns to forecast future events [
4
,
5
].
For modeling to more precisely forecast investor trading habits and market movements,
these characteristics must be studied and understood [
6
]. Stock traders can make substantial
profits if they properly identify price patterns in stocks. As a result, forecasting future
patterns in the stock market is crucial for stock traders to make decisions [
7
]. To this line of
inquiry, numerous models have undergone extensive testing and retesting, and numerous
factors have been identified as possible sources of valuable data for price prediction [8].
Consequently, investors need an automated decision support system because it will
use many data to automatically analyze market movements, which are developed using
machine learning (ML) techniques. It is critical to find algorithms that can more accurately
forecast stock market patterns utilizing outside data, such as social media posts and
financial news. ML experts are very interested in this area because they believe that making
accurate stock predictions based on outside factors would boost investors’ earnings. In
the field of finance, in particular, the development of artificial intelligence has resulted in
an “overflow” of potentially informative independent variables because studies published
in scientific journals employ a growing number of variables to forecast a given financial
variable or to explain financial relationships [
8
]. It does, however, assume that there might
be some inefficiency in the near run. On the other hand, technical analysis uses past data
to identify trends and forecast a stock’s future price moves. Unlike fundamental analysis,
this method mostly concentrates on the near future. The stock price prediction task was
defined as a time series forecasting problem by many scholars [9].
ML approaches have garnered increasing attention in recent times. The primary reason
is that these strategies work better with complex data that have non-linear relationships
than traditional methods do. Further, the vast amount of data produced by stock markets
insisted the researchers adopt the ML approaches to carry out the investment decisions,
where Support Vector Machine (SVM) [
5
], Logistic Regression, Hidden Markov Model
(HMM), and other conventional ML models are also utilized for the prediction of stock
markets. Even though the aforementioned techniques have attained considerable progress,
the bottleneck produced by the high frequency and uncertainty of the stock market time
series still results in unsatisfactory performance. More specifically, the Deep Learning (DL)
models mainly focus on replicating the accuracy of time series data, which often confuses
the model with the data appearance for a period, leading to wrong decisions. For instance,
the driving force behind similar upward trends in stocks is predicted to be high profitability,
but the future trends driven by these states generally vary with the prediction [
10
]. In order
to address these challenges, portfolio algorithms were utilized [
11
,
12
], in which two factors,
expected returns and risks, are crucial to allocating stocks among a variety of assets. The
general tendency of investors is to reduce risks and maximize returns. Meanwhile, the big
rewards also usually mean increased risks. Moreover, it is difficult to configure a function
or system that can precisely predict the variation of stock prices with high accuracy due
to the volatility, complexity, and nonlinearity in the stock prices. Further, stock prices are
impacted by several external factors, including political, economic, or social news, as well
as public sentiments, which limit the overall prediction [13].
To address the above limitations in the existing techniques, this research aims to fore-
cast the stock movement using the proposed AR-ERLM model, combining the advantages
of ARIMA, the Light gradient Boosting Machine (LightGBM), and the Recurrent Neural
Network (RNN). The utilization of technical indicators enhances the model's forecasting
ability in real-time data by reducing computational strain and improving forecast accuracy.
Furthermore, the proposed ensemble approach is reliable for short-term predictions and
offers more flexibility in capturing complex patterns as well as handling large datasets. The
key contributions are as follows.

Systems 2025,13, 162 3 of 28
•
Autoregressive integrated moving average ensemble recurrent light gradient boosting
machine (AR-ERLM): The ensemble AR-ERLM model combines the strengths of
decision trees and gradient boosting, resulting in accurate predictions. Furthermore,
the RNN can learn long-term dependencies, allowing them to capture patterns over
extended periods and automatically extract relevant features, which reduces the need
for manual feature extraction.
The article’s remaining sections are structured as follows: Section 2explores the
review of the literature, and Section 3describes the proposed methodology for stock
movement prediction. The research findings, performance, and comparative evaluations of
the AR-ERLM model are demonstrated in Section 4. Section 5concludes the research with
future works.
2. Literature Review
The literature papers related to Stock Movement Prediction are categorized, and the
merits and demerits are described as follows:
(i)
Statistical models
Jiang et al. [
14
] utilized the ARIMA model for estimating future stock price values.
Since ARIMA is highly adept at handling time series data, the model has shown superior
prediction outcomes, making it a good choice for predicting the future stock index. The
significance of stock price forecasting lies in the model’s prediction to mitigate losses mostly
caused by faulty intuitions and blind investment.
Constandina Koki et al. [
15
] suggested the Bayesian Hidden Markov Model for pre-
dicting the cryptocurrency price. The NHHM model relies conditionally on the hidden
states and determines the predictors with diverse linear and non-linear effects on the cryp-
tocurrency returns. Further, the model demonstrates that the dominance of the predictive
densities depends on the states that were captured in alternating periods with distinct
return characteristics. However, frequent changes between the hidden states were found in
all three time series, as the transitional patterns were markedly different.
(ii)
Machine Learning models
The ML method was used by Kittipob Saetia et al. [
6
], who analyzed the stock move-
ment prediction from the technical indicators dataset. The ML model was highly capable
of making out stocks with high future price growth in every aspect. However, the Pearson
correlation coefficient was the only technique used to evaluate the relation between the
stock movements and the keywords. Wasiat Khan et al. [
7
] employed an ML algorithm
to improve the performance and quality of predictions, feature selection, and spam tweet
reduction. The model has only the limited systematic techniques that were used for influ-
ential stocks relevant keywords while searching data on social media and news as well
as for stock market forecast. Jordan Ayala et al. [
9
] provided an ML technique combined
with Technical Analysis Indicators for stock movement prediction. The Technical indicator
calculates the evaluation of the stock price. In this model, the decision-making workflow of
trading has been used to evaluate the purchase and selling ratio of the stock value data.
The executed model used a lesser amount of metrics than many others available. Kyung
Keun Yun et al. [
13
] presented a hybrid GA-XGBoost technique to predict stock movements.
The method was executed along with a three-stage feature engineering process, which
achieved better results with more flexibility as the prediction time can be altered randomly.
Technical indicator’s predefined numbers are only used in this method. However, the
prediction model’s hyperparameters and model optimization should be improved for
better performance and results.

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Wei Chen et al. [
11
] implemented a portfolio construction technique using the ML-
based prediction of Shanghai Stock Exchange asset data. The prediction model was de-
veloped using hybrid XGBoost, IFA, and mean-variance (MV) models to predict the stock
movement more effectively than other traditional methods. The utilized dataset was highly
affected by various economic backgrounds and political environments, which impacted the
performance of the predictive model.
(iii)
Deep Learning models
Farnoush Ronaghi et al. [
14
] have established a hybrid deep-learning technique for
stock movement forecasting. The established methods were used to compare the different
classification metrics that calculate account productivity and cost levels of transactions to
analyze the economic gains in stock market prediction. Additionally, this model can reduce
the level of unneeded information and then potentially give better prediction results. The
BiLSTM model has allowed for the learning of many more complex data structures, which
also causes overfitting. Yaohu Lin et al. [
5
] utilized a hybrid deep learning technique to
improve the prediction of the stock market movement. This presented technique performed
exceptionally in both individual stock and multiple stock data based on their forecasting
framework, and the given results have more précised values in every testing case. However,
the executed method was not suited for predicting large-scale stock data. A DL method was
modeled by Shuting Dong et al. [
16
] for stock movement prediction. For stock movement
forecasting, the prediction model was dynamically evaluated and chosen via the dynamic
predictor selection algorithm (DPSA). The time taken by the established method to train
the networks and assess prediction performance was negligible. Additionally, compared to
other traditional systems, this one achieved the best accuracy and highest return value since
it made use of vast amounts of real-life financial time series data from the various stock
markets. The daily upward and downward trend of the equities might not be predictable
using the DPSA approach.
(iv)
Transformer Models
Chaojie Wang et al. [
17
] implemented the modern DL-based Transformer framework,
which exploited the encoder–decoder architecture for predicting the stock market index.
In this model, the transformer was initially utilized for the natural language processing
problem and further adopted for time series forecasting. Compared with the typical CNN
and RNN models, the Transformer model excels in its ability to extract crucial features,
thereby obtaining efficient predictions. Still, there exist limitations as this approach only
takes account of the single stock market index prediction, which is only one-dimensional
time series data.
Zicheng Tao et al. [
18
] developed the Series decomposition Transformer, which uses
the series decomposition layers and period-correlation mechanism to explore the relation-
ship between historical series. In addition, the model effectively learned the alterations in
the trends of the stock market, which resulted in high prediction performance and gener-
alizability. However, the social information prevalent in multiple sources was difficult to
collect, and a high level of uncertainty exists that affects the model’s prediction for different
stock markets.
2.1. Challenges
•
In the process of predicting financial variables, the existing large number of high
correlation features contains a minimal amount of information, which increases the
time complexity [14];
•
The SVM approach proved to be computationally expensive for voluminous datasets
and unsuitable for forecasting extensive stock data [5];

Systems 2025,13, 162 5 of 28
•
The development of incorporating the market stock prices introduced obstacles such
as misspellings, information duplication in text data, and shortcuts, causing low
efficiency in output results [9];
•
The DPSA model has limited ability to predict the daily downward and upward
stock trends [15];
•
The layered architecture in the ConvLSTM model increases thecomputational expenses
and requires careful tuning [8];
•
However, the proposed approach addressed the aforementioned challenges in the
existing techniques via the application of the AR-ERLM model. Specifically, the AR-
ERLM hybridizes the synergic strength of individual models, such as the potential
of ARIMA for determining the linear dependencies, the ability of RNN to capture
temporal dynamics, and LightGBM’s capability in handling the large-scale datasets
and their non-linear relationships for achieving the effective stock price prediction.
Consequently, the proposed approach improves the predictive accuracy, eliminates
overfitting, and minimizes the computational overhead.
2.2. Problem Statement
Predicting stock market trends is a difficult but significant problem. The underlying
nature of the stock market as a chaotic, noisy, dynamic, non-linear, and non-stationary
system is the main reason for this. The financial system is inclined by a variety of in-
terconnected and interplaying elements, such as general economic conditions, political
developments, and trader expectations [
2
]. As a result, prediction of the stock movement
trend index is very challenging and is still regarded as a significant time series research is-
sue [
8
]. While the existing stock movement prediction tasks provide better results, they pose
certain challenges, such as data overfitting, time complexity, and performance degradation
problems [
6
]. Therefore, to mitigate these issues, this research proposes the AR-ERLM
framework for effective stock movement prediction. Specifically, the proposed approach
makes use of the ARIMA model to capture the linear dependencies in time series data, mak-
ing the proposed approach effective for modeling stock prices that often show variations in
trends and seasonality. Meanwhile, the RNN learns the long-term dependencies, facilitating
the model to capture intricate patterns over a long time and eliminate the requirement
for manual feature extraction. Ultimately, the ensemble AR-ERLM model integrates the
potential of decision trees and gradient boosting in Light GBM for making accurate stock
movement predictions [19].
3. Proposed AR-ERLM Model for Stock Movement Prediction
The key objective of the research is to effectively forecast stock movements using the
AR-ERLM model. Initially, the Google trends data and the stock movements are collected
from the live stream dataset [
20
–
22
]. Then, the Google trends and stock market data are
combined using the daily and weekly binary calculations, which are then provided in
the preprocessing stage, where data cleaning is performed. From the preprocessed data,
the technical indicators are calculated, which is then subjected to the proposed AR-ERLM
model, which leverages the benefits of ARIMA, which is a statistical model for time series
analysis, RNN for capturing the temporal dynamics, and LightGBM for capturing the
non-linear relationships in the complex time series data along with effectively handling
the large-scale datasets. The proposed ensemble model effectively predicts stock market
movement with better accuracy. The schematic illustration of the AR-ERLM model for
stock movement prediction is illustrated in Figure 1.

Systems 2025,13, 162 6 of 28
Systems 2025, 13, 162 6 of 30
LightGBM for capturing the non-linear relationships in the complex time series data
along with effectively handling the large-scale datasets. The proposed ensemble model
effectively predicts stock market movement with better accuracy. The schematic illustra-
tion of the AR-ERLM model for stock movement prediction is illustrated in Figure 1.
Figure 1. Flow diagram of the AR-ERLM model for stock movement prediction.
3.1. Input for Stock Movement Prediction
In this research, the Google trends data and the stock market data of Amazon [20],
Meta [21], and Netflix [22] are collected from Yahoo Finance, which is used to forecast
stock movements. Further, these datasets comprise the history of daily prices of stocks
such as Date field, open price, high price, low price, closing price, adjusted closing price,
and trading volume attribute.
3.1.1. Stock Market Data
The data comprise high, low, volume, open, and close. Any listed stock’s opening
price is its price at the beginning of the trading day. The lowest and highest price of
stocks on that particular day is represented by the high and low values. The stock price
at the end of the trading day is known as the closing price. Since the adjusted close price
represents the stock’s value after shares are paid, it is recognized as the true price of that
stock. Numerous factors affect stock prices, which are frequently used as indicators to
examine market behavior. Therefore, analyzing technical indicators using the prices of
securities increases the effectiveness of the understanding of market activity.
3.1.2. Google Trends Data
Google trends data
Stock market data
Daily and weekly
rolling binary
calculation
Data preprocessing
AR-ERLM model
Predicted
stock
movement
Technical
indicators
Figure 1. Flow diagram of the AR-ERLM model for stock movement prediction.
3.1. Input for Stock Movement Prediction
In this research, the Google trends data and the stock market data of Amazon [
20
],
Meta [
21
], and Netflix [
22
] are collected from Yahoo Finance, which is used to forecast stock
movements. Further, these datasets comprise the history of daily prices of stocks such
as Date field, open price, high price, low price, closing price, adjusted closing price, and
trading volume attribute.
3.1.1. Stock Market Data
The data comprise high, low, volume, open, and close. Any listed stock’s opening
price is its price at the beginning of the trading day. The lowest and highest price of
stocks on that particular day is represented by the high and low values. The stock price
at the end of the trading day is known as the closing price. Since the adjusted close price
represents the stock’s value after shares are paid, it is recognized as the true price of that
stock. Numerous factors affect stock prices, which are frequently used as indicators to
examine market behavior. Therefore, analyzing technical indicators using the prices of
securities increases the effectiveness of the understanding of market activity.
3.1.2. Google Trends Data
Google launched a service called Google Trends to assist in determining the popularity
of terms such as brands, products, or websites. Users can view the popularity of these
phrases in addition to the daily popular trends. Google Trends is intended for users who
rely on or benefit from trends, whether they are marketers, operators of online stores, or
even individuals who want to start a vlog but do not know what to sell or how to find the

Systems 2025,13, 162 7 of 28
most searched terms every day or month. It also aids in the methodical formulation of
marketing strategies and commercial plans.
3.2. Daily and Weekly Rolling Binary Calculation
In this research, the weekly trends represent the stock market trends that the general
direction of the market price varying over time, and it is based on the demand for the four
prominent tech stocks such as Amazon, Meta platform, Netflix, and Nifty50 are analyzed.
Additionally, the daily prices of the stocks were obtained from Yahoo Finance. To improve
prediction accuracy, the rolling binary calculation method is employed, which converts
weekly trends into daily data and allows the capture of finer fluctuations. Furthermore,
this research utilizes the real-time live dataset and is applicable for real-time prediction of
stock movements. To determine the periods of important price declines from the historical
time series data, the ratio of the current index level at time
t
to the maximum index level
over
q
rolling periods prior to time
t
is utilized, and transformed the index level series to
the Maximum Level MaxL sequence as follows:
MaxLt=Gt/maxGt−q,Gt−q+1, . . . Gt(1)
where
Gt
denotes the closing price. In this stock movement prediction, one year is set as
the rolling period for evaluating the above ratio. For instance, the ratio of 100% represents
that the index level grows to the maximum value in the rolling period. Meanwhile, the low
value of
MaxL
denotes the decline in price over the rolling period. Further, the binary crisis
variable is developed considering the sequence of cutoff values, which requires taking the
difference between the moving averages of the ratio and the factor of moving standard
deviations. Further, the binary crisis indicator is expressed as follows:
cct=(1i f M axLt<MaxLt−2.5σt
0otherwise (2)
where
σt
indicates the standard deviation over the rolling period,
MaxLt
represents the
mean value of
MaxL
ranging from
t−q
to
t−
1. In Equation (2), the mean value and the
standard deviation are calculated for the first 250 trading days. Further, the first day of the
sample is subtracted, and an extra day is added at a time to evaluate the statistics in each of
the following days.
3.3. Data Preprocessing
Preparing raw data for analysis, particularly for market movement prediction, requires
data preprocessing. Here, data cleaning is performed to identify and remove irrelevant
data, including dates that do not contribute to the analysis. Data preprocessing ensures
data quality and reliability, leading to better decision-making.
3.4. Technical Indicators
Technical indicators are helpful in forecasting asset prices in the future, which is
important for incorporating them into automated trading systems. Technical indicators
are frequently employed by active traders designed to assess short-term price movements.
However, long-term investors can also utilize technical indicators to identify entry and
exit locations.

Systems 2025,13, 162 8 of 28
3.4.1. Moving Average
The MA uses the average closing price over a given period to produce moving aver-
ages, smooths and filters numerous aberrant signals to show the average trend over that
period, which is defined as
IMA =Gt+Gt−1+Gt−2+. . . Gt−n+1
n(3)
where nindicates the time interval and the close price is signified as G.
3.4.2. Bollinger Bands (BB)
The BB is a volatility indicator that tracks an upper and lower band utilizing two
standard deviations.
3.4.3. Relative Strength Index (RSI)
RSI helps gauge market momentum by assigning a value between 0 and 100 that
indicates whether an asset is overbought or oversold.
IRS I (t)=100 ∗UAvg(t)
UAvg +DAvg
(4)
where
UAvg
,
DAvg
indicates the upward and the downward average price movement, respectively.
3.4.4. Money Flow Index (MFI)
The MFI measures the flow of money in and out of security, which is mathematically
calculated as follows:
IMF I (t)=100 −100
1+MR(t)(5)
where MR(t)denotes the money ratio.
3.4.5. Average True Range (ATR)
ATR breaks down the whole range of a stock’s or asset’s price over a given period to
determine the volatility of finance markets.
IATR (t)=1
n
n
∑
j=1
TR(t−j+1)(6)
where TR indicates the true range.
3.4.6. Force Index
The volume, magnitude, and direction of the stock price change are all considered by
the force index. These three components combine to create an oscillator that gauges the
pressure to purchase and sell.
3.4.7. Ease of Movement Value (EMV)
An oscillator called EMV aims to combine volume and price into a single quantity.
Assessing the strength of a trend is helpful because it considers both price and volume.
3.4.8. Aroon Indicator
Aroon indicator [
23
] is used to spot shifts in an asset’s price trend and gauge the
strength of the trends. The indicator counts the intervals between highs and lows for a
given period.

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3.4.9. Aroon up Channel
The strength of the uptrend is measured by the Aroon up channel, which is represented
as follows:
IAup =CP −NPdays
CP ∗100 (7)
where
CP
indicates the calculation period, and
NPd ays
represents the number of days
following the highest price.
3.4.10. Aroon Down Channel
The strength of the downtrend is measured by the Aroon down channel, which is
represented as follows:
IAup =CP −NLdays
CP ∗100 (8)
where NLdays denotes the number of days following the lowest price.
3.4.11. MA Convergence Divergence (MACD)
MACD is defined as the difference between the two exponential moving averages [
24
],
which can be evaluated as follows:
IMACD(t)=
n
∑
i=1
IEM A12d−
n
∑
i=1
IEM A26d(9)
where IEM A denotes the exponential moving average.
3.4.12. MACD Histogram
The MACD’s background includes a histogram, which shows the difference between
the signal line (SL)and the MACD that is mathematically defined as
HMACD =lineM ACD −SL (10)
where lineMACD denotes the MACD line.
3.4.13. MACD Signal Line
The signal line serves as the basis for interpretation. When the MACD is above the
signal line, the bar is positive; when the MACD is below the signal, it is negative.
3.4.14. Exponential Moving Average (EMA)
The EMA is a technical indicator that is employed to track the price of a stock.
IEM A(t)=2
n+1Gtn−1
n+1IEM A(t−1)(11)
where Gtrepresents the index value at the time t.
3.4.15. Simple Moving Average (SMA-50)
SMA is computed by dividing the average of a given range of prices and the total
number of periods within that range.
ISM A(t)=1
n(Z∗IMA (t)) +(n−Z)∗ISMA (t−1)(12)
where Zindicates the weights.
3.4.16. SMA-200
The SMA 200 is computed using the average price of the last 200 days with the daily
price chart as well as other MA.

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3.4.17. Weighted Moving Average (WMA)
The WMA assigns more weight to the present data, which is used to determine the
trade trends.
3.4.18. Triple Exponential Average (TRIX)
The TRIX is also used as a momentum indicator, which determines the percentage
change of moving averages as well as the difference between the smoothed version of
price information.
3.4.19. Mass Index
The mass index is used to forecast the trend reversal, which is measured between the
range of high and low stock prices.
3.4.20. Ichimoku Kinko Hyo Span A
Ichimoku means one look in Japanese, which implies that traders simply need to
glance at the chart to identify momentum, support, and resistance. Senkou Span A, often
known as Leading Span A, is one of the Ichimoku Cloud indicator’s five components. The
Leading Span A line is a momentum indicator that can suggest trades depending on levels
of support and resistance.
3.4.21. Ichimoku Kinko Hyo Span B
A Kumo is a cloud formation that is created when the Leading Span B and the Senkou
Span A line combine. Levels of resistance and assistance are offered by the cloud.
3.4.22. Know Sure Thing (KST)
To predict the momentum of price movements in several markets, they are identified
using the KST indicator.
3.4.23. Detrended Price Oscillator (DPO)
To measure the distance between the peaks and troughs in the price/indicator. DPO
helps traders predict future peaks in selling and buying opportunities.
3.4.24. Commodity Channel Index (CCI)
CCI is used to evaluate the variation between the current and the historical average
price, which can be mathematically computed as
ICCI =
ht+lowt+Gt
3−IMA (n)
0.015 ∗1
n∑n
i−nIMA (i)−Gi
(13)
where ht,lowtindicates the high and low prices, respectively.
3.4.25. Average Directional Index (ADX)
The ADX is an oscillator that measures the strength of trends. The mathematical
equation for ADX is defined as follows:
IADX (t)=IADX(t−1)∗(n−1)+IDX(t)
n(14)
where ndenotes the period and IDX(t)indicates the directional movement index.

Systems 2025,13, 162 11 of 28
3.4.26. Minus Directional Indicator (–DI)
The presence of a downtrend is measured using –DI, which is described using the
following equation:
−IDI =Sm −DM
TR (15)
where
−DM
represents the negative directional movement,
Sm
indicates the smoothened
value.
3.4.27. Plus Directional Indicator (+DI)
The presence of an uptrend is measured using +DI, which is described using the
following equation
+IDI =Sm +DM
TR 100 (16)
3.4.28. Schaff Trend Cycle (STC)
STC is used to calculate the velocity of price movements. Further, the obtained
technical indicators assist in identifying the potential reversal points and trend direction as
well as provide more statistical parameters for evaluation. In this research, the technical
indicators are fed into the proposed AR-ERLM model to make predictions about the
stock movement.
3.5. Autoregressive Integrated Moving Average Ensemble Recurrent Light Gradient Boosting
Machine for Stock Movement Prediction
Stock movement forecasting is a major task in the economic world, but because of the
non-linear characteristics of data, it remains challenging. Several ML and DL approaches
have been developed in recent years; while the established techniques attained better results,
they also posed certain inherent limitations. The XGBoost was an effective ML technique
mostly used by various authors [
9
,
11
,
13
], which provides accurate predictions due to its
ensemble of decision trees and regularization techniques. It also handles noise and outliers
well, making it suitable for stock movement prediction tasks. However, XGBoost does
not directly handle categorical features and can be memory-intensive for large datasets.
Furthermore, the convolutional neural network with long short-term memory (CNN-
LSTM) was utilized by previous studies [
8
,
14
] to significantly obtain pertinent features
from raw data, while LSTM captures temporal dependencies that also modeled complex,
non-linear relationships in stock data. Nevertheless, combining CNN and LSTM introduced
additional complexity, which required careful tuning. Training could be computationally
expensive due to the layered architecture. The random forest [
3
] classifier designed for stock
movement prediction handles noise and outliers well, making it subtle for stock prediction,
which also requires minimal parameters for training as well as effectively handling large
datasets. Despite their advantages, the linear assumptions did not capture the dynamic
nature of stock market data. Artificial Neural Networks (ANN) [
25
] could capture complex
patterns and non-linear relationships as well as handle different data styles and structures.
However, if not properly regularized, the ANN technique was prone to overfitting.
To overcome the above-mentioned limitations of the existing techniques, this research
presented an AR-ERLM model that is designed using the ensemble LightGBM and RNN
classifiers and utilizes the ARIMA features for effective stock movement prediction. ARIMA
captures trends and seasonality in time series data. Further, the RNN-LightGBM handles
non-linear relationships and feature extraction. The architecture of the AR-ERLM model
for stock movement prediction is shown in Figure 2.

Systems 2025,13, 162 12 of 28
Systems 2025, 13, 162 12 of 30
memory (CNN-LSTM) was utilized by previous studies [8,14] to significantly obtain per-
tinent features from raw data, while LSTM captures temporal dependencies that also
modeled complex, non-linear relationships in stock data. Nevertheless, combining CNN
and LSTM introduced additional complexity, which required careful tuning. Training
could be computationally expensive due to the layered architecture. The random forest
[3] classifier designed for stock movement prediction handles noise and outliers well,
making it subtle for stock prediction, which also requires minimal parameters for train-
ing as well as effectively handling large datasets. Despite their advantages, the linear as-
sumptions did not capture the dynamic nature of stock market data. Artificial Neural
Networks (ANN) [25] could capture complex patterns and non-linear relationships as
well as handle different data styles and structures. However, if not properly regularized,
the ANN technique was prone to overfitting.
To overcome the above-mentioned limitations of the existing techniques, this re-
search presented an AR-ERLM model that is designed using the ensemble LightGBM
and RNN classifiers and utilizes the ARIMA features for effective stock movement pre-
diction. ARIMA captures trends and seasonality in time series data. Further, the RNN-
LightGBM handles non-linear relationships and feature extraction. The architecture of
the AR-ERLM model for stock movement prediction is shown in Figure 2.
Figure 2. AR-ERLM model architecture combining the ARIMA statistical analysis technique for
feature extraction and the LightGBM and RNN techniques for prediction.
Initially, the technical descriptors obtained from the input data are provided in the
ARIMA model, which is a significant technique used in prediction tasks of time series
analysis, also known as the Box–Jenkins method. ARIMA is a technique that synthesizes
historical data patterns to produce forecasts. When it comes to forecasting, parameter es-
timation, and univariate time series model identification, the ARIMA approach gives a
great deal of versatility [26]. The generated time series is derived as follows [27]:
01122 1122
...... .....
tttQtQtttPtP
ggg g
θ
φφ φ ξ
θ
ξ
θ
ξ
θ
ξ
−− − −− −
=+ + + +− − − (17)
RNN
LightGBM
ARIMA
H Ht-1 Ht Ht+1 …
Prediction
output
Input
Figure 2. AR-ERLM model architecture combining the ARIMA statistical analysis technique for
feature extraction and the LightGBM and RNN techniques for prediction.
Initially, the technical descriptors obtained from the input data are provided in the
ARIMA model, which is a significant technique used in prediction tasks of time series
analysis, also known as the Box–Jenkins method. ARIMA is a technique that synthesizes
historical data patterns to produce forecasts. When it comes to forecasting, parameter
estimation, and univariate time series model identification, the ARIMA approach gives a
great deal of versatility [26]. The generated time series is derived as follows [27]:
gt=θ0+ϕ1gt−1+ϕ2gt−2+. . . . . . ϕQgt−Q+ξt−θ1ξt−1−θ2ξt−2−. . . . . . θPξt−P(17)
where
gt
signifies the stationary value series,
ξt
indicates the random error at
t
, the model
parameters are signified as
ϕi(i=1, 2, . . . Q)
and
θl(l=1, 2, . . . P)
. The integers
Q
and
P
are frequently referred to as the model’s order. It is assumed that random errors ξthave a
mean of zero and a constant variance of
σ2
. They are also assumed to be identically and
independently distributed. For an ARIMA model to be effective in forecasting, stationary
is a prerequisite. The feature of a stationary time series is that it maintains consistent
statistical properties throughout time, such as the mean and the autocorrelation structure.
When the observed time series shows heteroscedasticity and trend, differencing and power
transformation are often used to the data to remove trends and stabilize variance before an
ARIMA model can be fitted. Estimating the model parameters is simple, and to minimize
the overall measure of errors, the parameters are calculated using the non-linear optimiza-
tion technique. The output obtained from the ARIMA model
(gt)
is provided as input for
both LightGBM and RNN models simultaneously.
LightGBM uses a tree-based learning algorithm created by Microsoft. LightGBM
uses gradient-based one-side sampling (GOSS) and exclusive feature bundling (EFB) to
shorten training times without sacrificing accuracy. Additionally, it builds trees using a leaf-
wise growth strategy and histogram-based techniques for data binning, leading to faster
convergence and improved performance [
28
]. A technique for effective gradient boosting
with big datasets is called GOSS, which involves sampling the data points according

Systems 2025,13, 162 13 of 28
to their gradients, and the probability of small data points being selected in training
is lower. Consequently, GOSS lowers the quantity of data points needed for training
without compromising the model’s overall performance. In contrast, EFB is a feature
bundling technique that reduces the number of features utilized for training by combining
related characteristics. EFB can assist in lowering the computational cost of training and
increase model accuracy by grouping features [
29
]. GOSS and EFB, when coupled with
other methods such as leaf-wise tree growth and histogram-based binning, have enabled
AR-ERLM to attain better performance in stock movement prediction tasks, particularly
for high-dimensional and large-scale datasets. By using the
R
additive functions of the
LightGBM, the AR-ERLM model can predict the outcome, which is detailed as follows [
30
]:
ˆ
zt=
R
∑
j=1
fj(gt),fj∈F(18)
Here, fjdenotes the function in the functional space F, which can be expressed as
fj(gt)=ud(gt),u∈RN,d:Rm→{1, 2, . . . N}(19)
where
N
denotes the number of leaves,
u
represents vector sores on leaves, and
d
is
a function that links each data point to its corresponding leaf. The set of all potential
functions based on various pairings of
d
and
u
is captured by
F
. The objective function
(O)
that needs to be optimized is derived as follows:
O=
n
∑
k=1
L(zt,ˆ
zt)+
R
∑
j=1
ϖfj(20)
where the regularization term
ϖfj
is used to penalize the model’s complexity and
L
is a
loss function that quantifies the variation between the raw prediction
ˆ
zt
and the target
zt
.
The regularization term can be defined as
ϖfj=λN+1
2γ
R
∑
j=1
u2
j(21)
where
γ
and
λ
indicates the learning parameters. AR-ERLM uses histogram-based
techniques to bin data into discrete intervals, which lowers computing costs and
memory utilization.
RNN is a variant of neural networks where the units are connected recurrently, en-
abling them to process the incoming sequence using their internal memory. This makes
it possible to employ AR-ERLM for the stock market prediction tasks. In this research,
AR-ERLM is employed because stock data requires consideration of long-term dependen-
cies [
31
] in the data. The computing units of the model have a configurable weight and
real-valued activation that varies over time. The same set of weights is applied recursively
over a structure resembling a graph to construct AR-ERLM. The input
gt
at the current time
step and the preceding hidden state Ht−1are used to evaluate the hidden state.
Ht=tanh(pgt+q Ht−1+b)(22)
Yt=tanh(wHt+c)(23)
where
Yt
denotes the output, RNN-trained input-to-hidden, hidden-to-hidden, and hidden-
to-output parameters are
p
,
q
, and
w
, respectively. Because the learned model in an
AR-ERLM is defined in terms of the transition from one state to another, it always has the
same input size. Additionally, for each time step, the design employs the same transition
function with the same parameters. To provide the final prediction output
(Dt)
, the AR-
ERLM model combines the output of both models using the following equation:

Systems 2025,13, 162 14 of 28
Dt=Yt⊕ˆ
zt(24)
where the symbol ⊕indicates the concatenation operation.
The AR-ERLM model predicts the stock movement effectively. The proposed model
excels in capturing linear relationships and trends in time series data, while the RNN
is adaptable at learning from sequential data with their internal memory, making them
suitable for recognizing patterns over time. In addition, the gradient boosting technique
effectively handles large datasets and improves performance through its tree-based learning
techniques. Therefore, the AR-ERLM model predicts stock with better accuracy.
4. Results and Discussion
The experimental results evaluated using the AR-ERLM model for stock movement
prediction, as well as the comparative and performance analysis, are described in the
following section.
4.1. Experimental Setup
The research for stock movement prediction using the AR-ERLM model is conducted
in Python software V 3.10 on a Windows 10 operating system with 16 GB of RAM. The
initial parameter settings of the proposed network involve a batch size of 32, a learning
rate of 0.001, a dropout rate of 0.02, a linear activation function, and a loss function “MSE”,
optimized utilizing the default optimizer, Adam.
4.2. Performance Metrics
The performance of the AR-ERLM model in the stock movement prediction task is
analyzed using the following performance metrics: Mean Absolute Error (MAE), RMSE,
Mean Absolute Percentage Error (MAPE), and MSE. Outliers and imbalances in the dataset
can be found using MSE, which calculates the average of the squared discrepancies between
the actual and predicted values. The standard deviation of the error is measured by RMSE,
which is the square root of MSE and makes model comparisons simple. RMSE makes
it simple to compare model performances. The most accurate model is the one with the
lowest RMSE value. The error is expressed as a percentage of the actual value using MAPE.
4.3. Dataset Description
In this research, the weekly trends of three prominent technical stocks such as Ama-
zon [
20
], Meta platform [
21
], Netflix [
22
], and Nifty50 [
32
] are analyzed. Additionally,
the daily prices of the stocks were obtained from Yahoo Finance. Further, these datasets
comprise the history of daily prices of stocks such as Date field, open price, high price, low
price, closing price, adjusted closing price, and trading volume attribute to carry out the
implementation of the stock movement prediction. Further, the four stocks, including the
Amazon, Meta platform, Netflix, and Nifty50, are utilized for the prediction as the Netflix
stock operates as the world’s most-subscribed streaming service. In addition, the Meta
data and Amazon stocks are progressing and providing impressive returns, significantly
outperforming the e-commerce market. Meanwhile, the NIFTY 50 is an Indian stock market
index indicating the float-weighted average of 50 of the Major Indian companies listed on
the National Stock Exchange. Moreover, the proposed approach analyzed the stock data
collected from the current to the last 5 years to attain efficient stock movement prediction.
4.4. Comparative Methods
In this research, the performance of the AR-ERLM model is compared with the other
presented techniques such as XGBoost [
6
], Artificial Neural Network (ANN) [
25
], Im-
proved Firefly Algorithm enabled XGBoost (IFA-XGBoost) [
11
], Genetic Algorithm Light-

Systems 2025,13, 162 15 of 28
GBM (GA-LightGBM) [
33
], ARI-MA-LS-SVM [
34
], ANN-SVM [
35
], Convolutional LSTM
(ConvLSTM) [16].
4.4.1. Comparative Analysis for Meta Data Using Training Percentage
The comparative evaluation of the AR-ERLM model to predict stock movements using
the Meta data in terms of RMSE, MAPE, MAE, and MSE is depicted in Figure 3. For
the Training Percentage (TP) 90, the AR-ERLM model attained an MAE of 1.77, which is
comparably less than XGBoost by 0.14, ANN by 0.73, IFA-XGBoost by 0.23, GA-LightGBM
by 0.15, ARI-MA-LS-SVM by 0.15, ANN-SVM by 0.14, and ConvLSTM by 0.04. Simi-
larly, for the RMSE measure, the AR-ERLM model gets 2.53, which is reduced over the
traditional XGBoost by 0.02, ANN by 0.75, IFA-XGBoost by 0.22, GA-LightGBM by 0.04,
ARI-MA-LS-SVM by 0.022, ANN-SVM by 0.018, and ConvLSTM by 0.01. In terms of MSE,
the AR-ERLM model conquers a minimal value of 6.43, reduced by 0.13 over XGBoost,
4.34 over ANN,1.139 over IFA-XGBoost,0.21 over GA-LightGBM, 0.12 over ARI-MA-LS-
SVM, 0.11 over ANN-SVM, and 6.53 over ConvLSTM. Subsequently, the AR-ERLM model
attains the low error of 3.43, which is minimized by 0.20 over XGBoost, 1.54 over ANN,
1.28 over IFA-XGBoost, 0.97 over GA-LightGBM, 0.90 over ARI-MA-LS-SVM, 0.75 over
ANN-SVM, and 0.38 over ConvLSTM. From the comparative results, it is clear that the
AR-ERLM model efficiently predicts stock movements with minimal errors. Furthermore,
the proposed model excels in capturing linear relationships and trends in time series data,
while the RNN adapts to learning from sequential data with their internal memory, making
them suitable for recognizing patterns over time as well, and the gradient boosting tech-
nique effectively handles large datasets and improves performance through its tree-based
learning techniques.
Systems 2025, 13, 162 16 of 30
tionships and trends in time series data, while the RNN adapts to learning from sequen-
tial data with their internal memory, making them suitable for recognizing patterns over
time as well, and the gradient boosting technique effectively handles large datasets and
improves performance through its tree-based learning techniques.
MAE RMSE
MAPE MSE
Figure 3. Comparative analysis for Meta data using training percentage analysis.
4.4.2. Comparative Analysis for Amazon Data Using TP
The comparative analysis of the AR-ERLM model for predicting stock movements
using Amazon data, based on metrics such as RMSE, MAE, MAPE, and MSE, is deline-
ated in Figure 4. For TP 90, the AR-ERLM model achieved an MAE of 1.65, which is no-
tably lower than XGBoost by 0.13, ANN by 0.91, IFA-XGBoost by 0.20, GA-LightGBM by
0.17, ARI-MA-LS-SVM by 0.07, ANN-SVM by 0.05, and ConvLSTM by 0.01. Similarly,
the RMSE measure for the AR-ERLM model is 2.588, reduced over the traditional
XGBoost by 0.12, ANN by 0.84, IFA-XGBoost by 0.24, GA-LightGBM by 0.01, ARI-MA-
LS-SVM by 0.02, ANN-SVM by 0.03, ConvLSTM by 0.01. In terms of MSE, the AR-ERLM
model outperforms other established techniques with a minimal value of 6.702, obtain-
ing an error difference of 0.66 against XGBoost, 5.10 against ANN,1.30 against IFA-
XGBoost,0.09 against GA-LightGBM, 0.01 against ARI-MA-LS-SVM. In terms of MAPE,
the AR-ERLM model conquers a minimal value of 2.81 achieving the error difference of
1.86, 1.34, 1.14, 1.09, 0.67, 0.54, and 0.31 over the other established techniques such as
XGBoost, ANN, IFA-XGBoost, GA-LightGBM, ARI-MA-LS-SVM, ANN-SVM, and Con-
vLSTM, respectively. These comparative results highlight the efficacy of the AR-ERLM
Figure 3. Comparative analysis for Meta data using training percentage analysis.

Systems 2025,13, 162 16 of 28
4.4.2. Comparative Analysis for Amazon Data Using TP
The comparative analysis of the AR-ERLM model for predicting stock movements
using Amazon data, based on metrics such as RMSE, MAE, MAPE, and MSE, is delineated
in Figure 4. For TP 90, the AR-ERLM model achieved an MAE of 1.65, which is notably
lower than XGBoost by 0.13, ANN by 0.91, IFA-XGBoost by 0.20, GA-LightGBM by 0.17,
ARI-MA-LS-SVM by 0.07, ANN-SVM by 0.05, and ConvLSTM by 0.01. Similarly, the
RMSE measure for the AR-ERLM model is 2.588, reduced over the traditional XGBoost
by 0.12, ANN by 0.84, IFA-XGBoost by 0.24, GA-LightGBM by 0.01, ARI-MA-LS-SVM
by 0.02, ANN-SVM by 0.03, ConvLSTM by 0.01. In terms of MSE, the AR-ERLM model
outperforms other established techniques with a minimal value of 6.702, obtaining an
error difference of 0.66 against XGBoost, 5.10 against ANN, 1.30 against IFA-XGBoost,
0.09 against GA-LightGBM, 0.01 against ARI-MA-LS-SVM. In terms of MAPE, the AR-
ERLM model conquers a minimal value of 2.81 achieving the error difference of 1.86, 1.34,
1.14, 1.09, 0.67, 0.54, and 0.31 over the other established techniques such as XGBoost, ANN,
IFA-XGBoost, GA-LightGBM, ARI-MA-LS-SVM, ANN-SVM, and ConvLSTM, respectively.
These comparative results highlight the efficacy of the AR-ERLM model in predicting stock
movements with minimal errors. Additionally, the model excels in capturing linear rela-
tionships and trends in time series data, while RNNs are adept at learning from sequential
data due to their internal memory, making them suitable for recognizing patterns over
time. Meanwhile, the gradient boosting technique effectively handles large datasets and
enhances performance through its tree-based learning approach.
Systems 2025, 13, 162 17 of 30
model in predicting stock movements with minimal errors. Additionally, the model ex-
cels in capturing linear relationships and trends in time series data, while RNNs are
adept at learning from sequential data due to their internal memory, making them suit-
able for recognizing patterns over time. Meanwhile, the gradient boosting technique ef-
fectively handles large datasets and enhances performance through its tree-based learn-
ing approach.
MAE RMSE
MAPE MSE
Figure 4. Comparative analysis of Amazon data using training percentage analysis.
4.4.3. Comparative Analysis for Netflix Data
The comparative analysis of the AR-ERLM model for predicting stock movements
using Netflix data regarding metrics such as MAPE, MAE, RMSE, and MSE is delineated
in Figure 5. For TP 90, the AR-ERLM model achieved an MAE of 1.70, which is notably
lower than XGBoost by 0.12, ANN by 0.66, IFA-XGBoost by 0.15, GA-LightGBM by 0.12,
ARI-MA-LS-SVM by 0.08, ANN-SVM by 0.07. Similarly, the RMSE measure for the AR-
ERLM model is 2.38, showing an error difference of 0.2 over XGBoost, 0.49 over ANN,
0.30 over IFA-XGBoost, 0.23 over GA-LightGBM, 0.06 over ARI-MA-LS-SVM, 0.03 over
ANN-SVM, and 0.03 over ConvLSTM. In terms of MSE, the AR-ERLM model outper-
forms other established techniques with a minimal value of 5.66, reduced over the exist-
ing technique XGBoost by 0.123, ANN by 2.60, IFA-XGBoost by 1.54, GA-LightGBM by
Figure 4. Comparative analysis of Amazon data using training percentage analysis.

Systems 2025,13, 162 17 of 28
4.4.3. Comparative Analysis for Netflix Data
The comparative analysis of the AR-ERLM model for predicting stock movements
using Netflix data regarding metrics such as MAPE, MAE, RMSE, and MSE is delineated in
Figure 5. For TP 90, the AR-ERLM model achieved an MAE of 1.70, which is notably lower
than XGBoost by 0.12, ANN by 0.66, IFA-XGBoost by 0.15, GA-LightGBM by 0.12, ARI-MA-
LS-SVM by 0.08, ANN-SVM by 0.07. Similarly, the RMSE measure for the AR-ERLM model
is 2.38, showing an error difference of 0.2 over XGBoost, 0.49 over ANN, 0.30 over IFA-
XGBoost, 0.23 over GA-LightGBM, 0.06 over ARI-MA-LS-SVM, 0.03 over ANN-SVM, and
0.03 over ConvLSTM. In terms of MSE, the AR-ERLM model outperforms other established
techniques with a minimal value of 5.66, reduced over the existing technique XGBoost
by 0.123, ANN by 2.60, IFA-XGBoost by 1.54, GA-LightGBM by 1.17, ARI-MA-LS-SVM
by 0.29, ANN-SVM by 0.14, and ConvLSTM by 0.11. In terms of MAPE, the AR-ERLM
model conquers a minimal value of 3.05, achieving an error difference of 0.04 over XGBoost,
1.72 over ANN, 1.49 over IFA-XGBoost,0.59 over GA-LightGBM, 0.22 over ARI-MA-LS-
SVM,0.15 over ANN-SVM, and 0.019 over ConvLSTM. These comparative results highlight
the efficacy of the AR-ERLM model for stock movement prediction with minimal errors.
Additionally, the model excels in capturing linear relationships and trends in time series
data, while RNNs are adept at learning from sequential data due to their internal memory,
making them suitable for recognizing patterns over time. Meanwhile, the gradient boosting
technique effectively handles large datasets and enhances performance through its tree-
based learning approach.
Systems 2025, 13, 162 18 of 30
1.17, ARI-MA-LS-SVM by 0.29, ANN-SVM by 0.14, and ConvLSTM by 0.11. In terms of
MAPE, the AR-ERLM model conquers a minimal value of 3.05, achieving an error dif-
ference of 0.04 over XGBoost, 1.72 over ANN, 1.49 over IFA-XGBoost,0.59 over GA-
LightGBM, 0.22 over ARI-MA-LS-SVM,0.15 over ANN-SVM, and 0.019 over ConvLSTM.
These comparative results highlight the efficacy of the AR-ERLM model for stock
movement prediction with minimal errors. Additionally, the model excels in capturing
linear relationships and trends in time series data, while RNNs are adept at learning
from sequential data due to their internal memory, making them suitable for recogniz-
ing patterns over time. Meanwhile, the gradient boosting technique effectively handles
large datasets and enhances performance through its tree-based learning approach.
MAE RMSE
MAPE MSE
Figure 5. Comparative analysis of Netflix data using training percentage analysis.
4.4.4. Comparative Analysis for Nifty50 Using Training Percentage
The comparative evaluation of the AR-ERLM model with other existing methods
for predicting stock movements using Nifty50 data, in terms of metrics MAPE, MAE,
RMSE, and MSE, is illustrated in Figure 6. For 90% of training, the AR-ERLM model at-
tained the MAE score of 1.81, which is significantly lower than XGBoost by 0.45, ANN
by 0.72, IFA-XGBoost by 0.48, GA-LightGBM by 0.36, ARI-MA-LS-SVM by 0.24, ANN-
SVM by 0.08, and ConvLSTM by 0.05. Similarly, the RMSE for the AR-ERLM model is
2.39, outperforming the other existing techniques with the error difference of 0.66 over
XGBoost,0.67 over ANN, 0.59 over IFA-XGBoost,0.50 over GA-LightGBM, 0.49 over
Figure 5. Comparative analysis of Netflix data using training percentage analysis.

Systems 2025,13, 162 18 of 28
4.4.4. Comparative Analysis for Nifty50 Using Training Percentage
The comparative evaluation of the AR-ERLM model with other existing methods for
predicting stock movements using Nifty50 data, in terms of metrics MAPE, MAE, RMSE,
and MSE, is illustrated in Figure 6. For 90% of training, the AR-ERLM model attained the
MAE score of 1.81, which is significantly lower than XGBoost by 0.45, ANN by 0.72, IFA-
XGBoost by 0.48, GA-LightGBM by 0.36, ARI-MA-LS-SVM by 0.24, ANN-SVM by 0.08, and
ConvLSTM by 0.05. Similarly, the RMSE for the AR-ERLM model is 2.39, outperforming
the other existing techniques with the error difference of 0.66 over XGBoost,0.67 over ANN,
0.59 over IFA-XGBoost,0.50 over GA-LightGBM, 0.49 over ARI-MA-LS-SVM,0.30 over
ANN-SVM, and 0.13 over ConvLSTM. In terms of MSE, the AR-ERLM model surpasses
other existing techniques with a minimal value of 5.71, minimized over the other existing
technique XGBoost by 3.58, ANN by 3.64, IFA-XGBoost by 3.14, GA-LightGBM by 2.65, ARI-
MA-LS-SVM by 2.57, ANN-SVM by 1.51, and ConvLSTM by 0.65. In terms of MAPE, the
AR-ERLM model attains a minimal value of 2.54, achieving an error difference of 1.86 over
XGBoost, 4.93 over ANN, 3.76 over IFA-XGBoost, 2.20 over GA-LightGBM, 1.80 over
ARI-MA-LS-SVM, 1.76 over ANN-SVM, and 0.87 over ConvLSTM. From the comparative
evaluation, the AR-ERLM model attained minimal errors for stock movement prediction
due to its high potential in capturing the non-linear relationships and trends in complex
time series data. Moreover, the proposed approach attained low error values for the stock
movement prediction and outperformed other baseline techniques utilized for comparison.
Systems 2025, 13, 162 19 of 30
ARI-MA-LS-SVM,0.30 over ANN-SVM, and 0.13 over ConvLSTM. In terms of MSE, the
AR-ERLM model surpasses other existing techniques with a minimal value of 5.71, min-
imized over the other existing technique XGBoost by 3.58, ANN by 3.64, IFA-XGBoost
by 3.14, GA-LightGBM by 2.65, ARI-MA-LS-SVM by 2.57, ANN-SVM by 1.51, and Con-
vLSTM by 0.65. In terms of MAPE, the AR-ERLM model attains a minimal value of 2.54,
achieving an error difference of 1.86 over XGBoost, 4.93 over ANN, 3.76 over IFA-
XGBoost, 2.20 over GA-LightGBM, 1.80 over ARI-MA-LS-SVM, 1.76 over ANN-SVM,
and 0.87 over ConvLSTM. From the comparative evaluation, the AR-ERLM model at-
tained minimal errors for stock movement prediction due to its high potential in captur-
ing the non-linear relationships and trends in complex time series data. Moreover, the
proposed approach attained low error values for the stock movement prediction and
outperformed other baseline techniques utilized for comparison.
MAE RMSE
MAPE MSE
Figure 6. Comparative analysis of Nifty50 data using training percentage analysis.
Figure 6. Comparative analysis of Nifty50 data using training percentage analysis.

Systems 2025,13, 162 19 of 28
4.4.5. Comparative Analysis for Meta Data Using k-Fold
The comparative evaluation of the AR-ERLM model to predict stock movements using
the Meta data in terms of RMSE, MAPE, MAE, and MSE is depicted in Figure 7. For the
k-fold 10, the AR-ERLM model attained an MAE of 1.58, which is comparably less than
XGBoost by 0.20, ANN by 0.58, IFA-XGBoost by 0.45, GA-LightGBM by 0.26, ARI-MA-
LS-SVM by 0.15, ANN-SVM by 0.08, and ConvLSTM by 0.02. Similarly, for the RMSE
measure, the AR-ERLM model gets 2.47, which is reduced over the traditional XGBoost
by 0.06, ANN by 0.53, IFA-XGBoost by 0.33, GA-LightGBM by 0.29, ARI-MA-LS-SVM by
0.03, ANN-SVM by 0.029, and ConvLSTM by 0.02. In terms of MSE, the AR-ERLM model
conquers a minimal value of 6.10, reduced by 0.30 over XGBoost, 2.95 over ANN,1.76 over
IFA-XGBoost, 1.56 over GA-LightGBM,0.16 over ARI-MA-LS-SVM,0.14 over ANN-SVM,
and 0.10 over ConvLSTM. Subsequently, the AR-ERLM model attains the low error of 3.12,
which is minimized by 0.61 over XGBoost, 2.35 over ANN,1.29 over IFA-XGBoost, 1.02 over
GA-LightGBM, 0.80 over ARI-MA-LS-SVM, 0.37 over ANN-SVM, and 0.06 over ConvLSTM.
From the comparative results, it is clear that the AR-ERLM model efficiently predicts stock
movements with minimal errors. Furthermore, the proposed model excels in capturing
linear relationships and trends in time series data, while the RNN adapts to learning from
sequential data with their internal memory, making them suitable for recognizing patterns
over time as well, and the gradient boosting technique effectively handles large datasets
and improves performance through its tree-based learning techniques.
Systems 2025, 13, 162 21 of 30
MAE RMSE
MAPE MSE
Figure 7. Comparative analysis of Meta data using k-fold.
4.4.6. Comparative Analysis for Amazon Data Using k-Fold
The comparative analysis of the AR-ERLM model for predicting stock movements
using Amazon data, based on metrics such as RMSE, MAE, MAPE, and MSE, is deline-
ated in Figure 8. For k-fold 10, the AR-ERLM model achieved an MAE of 1.61, which is
notably lower than XGBoost by 0.50, ANN by 1.15, IFA-XGBoost by 0.94, GA-LightGBM
by 0.67, ARI-MA-LS-SVM by 0.10, ANN-SVM by 0.10, and ConvLSTM by 0.08. Similar-
ly, the RMSE measure for the AR-ERLM model is 2.35, reduced over the traditional
XGBoost by 0.33, ANN by 1.30, IFA-XGBoost by 1.03, GA-LightGBM by 0.69, ARI-MA-
LS-SVM by 0.28, ANN-SVM by 0.25, ConvLSTM by 0.22. In terms of MSE, the AR-ERLM
model outperforms other established techniques with a minimal value of 5.526, obtain-
ing an error difference of 1.70 against XGBoost, 7.85 against ANN, 5.91 against IFA-
XGBoost, 3.72 against GA-LightGBM, 1.39 against ARI-MA-LS-SVM. In terms of MAPE,
the AR-ERLM model conquers a minimal value of 2.81 achieving the error difference of
1.91, 1.67, 1.54, 1.53, 0.50, 0.73, and 0.44 over the other established techniques such as
XGBoost, ANN, IFA-XGBoost, GA-LightGBM, ARI-MA-LS-SVM, ANN-SVM, and Con-
vLSTM respectively. These comparative results highlight the efficacy of the AR-ERLM
model in predicting stock movements with minimal errors. Additionally, the model ex-
Figure 7. Comparative analysis of Meta data using k-fold.

Systems 2025,13, 162 20 of 28
4.4.6. Comparative Analysis for Amazon Data Using k-Fold
The comparative analysis of the AR-ERLM model for predicting stock movements
using Amazon data, based on metrics such as RMSE, MAE, MAPE, and MSE, is delineated
in Figure 8. For k-fold 10, the AR-ERLM model achieved an MAE of 1.61, which is notably
lower than XGBoost by 0.50, ANN by 1.15, IFA-XGBoost by 0.94, GA-LightGBM by 0.67,
ARI-MA-LS-SVM by 0.10, ANN-SVM by 0.10, and ConvLSTM by 0.08. Similarly, the
RMSE measure for the AR-ERLM model is 2.35, reduced over the traditional XGBoost
by 0.33, ANN by 1.30, IFA-XGBoost by 1.03, GA-LightGBM by 0.69, ARI-MA-LS-SVM
by 0.28, ANN-SVM by 0.25, ConvLSTM by 0.22. In terms of MSE, the AR-ERLM model
outperforms other established techniques with a minimal value of 5.526, obtaining an
error difference of 1.70 against XGBoost, 7.85 against ANN, 5.91 against IFA-XGBoost,
3.72 against GA-LightGBM, 1.39 against ARI-MA-LS-SVM. In terms of MAPE, the AR-
ERLM model conquers a minimal value of 2.81 achieving the error difference of 1.91, 1.67,
1.54, 1.53, 0.50, 0.73, and 0.44 over the other established techniques such as XGBoost, ANN,
IFA-XGBoost, GA-LightGBM, ARI-MA-LS-SVM, ANN-SVM, and ConvLSTM respectively.
These comparative results highlight the efficacy of the AR-ERLM model in predicting stock
movements with minimal errors. Additionally, the model excels in capturing linear rela-
tionships and trends in time series data, while RNNs are adept at learning from sequential
data due to their internal memory, making them suitable for recognizing patterns over
time. Meanwhile, the gradient boosting technique effectively handles large datasets and
enhances performance through its tree-based learning approach.
Systems 2025, 13, 162 22 of 30
cels in capturing linear relationships and trends in time series data, while RNNs are
adept at learning from sequential data due to their internal memory, making them suit-
able for recognizing patterns over time. Meanwhile, the gradient boosting technique ef-
fectively handles large datasets and enhances performance through its tree-based learn-
ing approach.
MAE RMSE
MAPE MSE
Figure 8. Comparative analysis of Amazon data using k-fold.
4.4.7. Comparative Analysis for Netflix Data Using k-Fold
The comparative analysis of the AR-ERLM model for predicting stock movements
using Netflix data regarding metrics such as MAPE, MAE, RMSE, and MSE is delineated
in Figure 9. For k-fold 10, the AR-ERLM model achieved an MAE of 1.51, which is nota-
bly lower than XGBoost by 0.05, ANN by 1.64, IFA-XGBoost by 0.79, GA-LightGBM by
0.71, ARI-MA-LS-SVM by 0.68, ANN-SVM by 0.33. Similarly, the RMSE measure for the
AR-ERLM model is 2.43, showing an error difference of 0.01 over XGBoost, 1.27 over
ANN, 0.59 over IFA-XGBoost, 0.44 over GA-LightGBM, 0.33 over ARI-MA-LS-SVM, 0.23
over ANN-SVM, and 0.08 over ConvLSTM. In terms of MSE, the AR-ERLM model out-
performs other established techniques with a minimal value of 5.92, reduced over the ex-
isting technique XGBoost by 0.07, ANN by 7.83, IFA-XGBoost by 3.23, GA-LightGBM by
2.38, ARI-MA-LS-SVM by 1.73, ANN-SVM by 1.20, and ConvLSTM by 0.40. In terms of
Figure 8. Comparative analysis of Amazon data using k-fold.

Systems 2025,13, 162 21 of 28
4.4.7. Comparative Analysis for Netflix Data Using k-Fold
The comparative analysis of the AR-ERLM model for predicting stock movements
using Netflix data regarding metrics such as MAPE, MAE, RMSE, and MSE is delineated in
Figure 9. For k-fold 10, the AR-ERLM model achieved an MAE of 1.51, which is notably
lower than XGBoost by 0.05, ANN by 1.64, IFA-XGBoost by 0.79, GA-LightGBM by 0.71,
ARI-MA-LS-SVM by 0.68, ANN-SVM by 0.33. Similarly, the RMSE measure for the AR-
ERLM model is 2.43, showing an error difference of 0.01 over XGBoost, 1.27 over ANN,
0.59 over IFA-XGBoost, 0.44 over GA-LightGBM, 0.33 over ARI-MA-LS-SVM, 0.23 over
ANN-SVM, and 0.08 over ConvLSTM. In terms of MSE, the AR-ERLM model outperforms
other established techniques with a minimal value of 5.92, reduced over the existing
technique XGBoost by 0.07, ANN by 7.83, IFA-XGBoost by 3.23, GA-LightGBM by 2.38, ARI-
MA-LS-SVM by 1.73, ANN-SVM by 1.20, and ConvLSTM by 0.40. In terms of MAPE, the
AR-ERLM model conquers a minimal value of 3.03, achieving an error difference of 0.89 over
XGBoost, 3.87 over ANN, 2.13 over IFA-XGBoost, 0.74 over GA-LightGBM, 0.60 over ARI-
MA-LS-SVM,0.48 over ANN-SVM, and 0.24 over ConvLSTM. These comparative results
highlight the efficacy of the AR-ERLM model for stock movement prediction with minimal
errors. Additionally, the model excels in capturing linear relationships and trends in time
series data, while RNNs are adept at learning from sequential data due to their internal
memory, making them suitable for recognizing patterns over time. Meanwhile, the gradient
boosting technique effectively handles large datasets and enhances performance through
its tree-based learning approach.
Systems 2025, 13, 162 23 of 30
MAPE, the AR-ERLM model conquers a minimal value of 3.03, achieving an error dif-
ference of 0.89 over XGBoost, 3.87 over ANN, 2.13 over IFA-XGBoost, 0.74 over GA-
LightGBM, 0.60 over ARI-MA-LS-SVM,0.48 over ANN-SVM, and 0.24 over ConvLSTM.
These comparative results highlight the efficacy of the AR-ERLM model for stock
movement prediction with minimal errors. Additionally, the model excels in capturing
linear relationships and trends in time series data, while RNNs are adept at learning
from sequential data due to their internal memory, making them suitable for recogniz-
ing patterns over time. Meanwhile, the gradient boosting technique effectively handles
large datasets and enhances performance through its tree-based learning approach.
MAE RMSE
MAPE MSE
Figure 9. Comparative analysis of Netflix data using k-fold.
4.4.8. Comparative Analysis for Nifty50 Using k-Fold
The comparative evaluation of the AR-ERLM model with other existing methods
for predicting stock movements using Nifty50 data, in terms of metrics MAPE, MAE,
RMSE, and MSE, is illustrated in Figure 10. With k-fold 10, the AR-ERLM model gained
an MAE score of 1.63, which is reduced over XGBoost by 0.23, ANN by 0.77, IFA-
XGBoost by 0.48, GA- LightGBM by 0.27, ARI-MA-LS-SVM by 0.20, ANN-SVM by 0.17,
and ConvLSTM by 0.10. Similarly, the RMSE for the AR-ERLM model is 2.45, outper-
Figure 9. Comparative analysis of Netflix data using k-fold.

Systems 2025,13, 162 22 of 28
4.4.8. Comparative Analysis for Nifty50 Using k-Fold
The comparative evaluation of the AR-ERLM model with other existing methods for
predicting stock movements using Nifty50 data, in terms of metrics MAPE, MAE, RMSE,
and MSE, is illustrated in Figure 10. With k-fold 10, the AR-ERLM model gained an MAE
score of 1.63, which is reduced over XGBoost by 0.23, ANN by 0.77, IFA-XGBoost by 0.48,
GA- LightGBM by 0.27, ARI-MA-LS-SVM by 0.20, ANN-SVM by 0.17, and ConvLSTM
by 0.10. Similarly, the RMSE for the AR-ERLM model is 2.45, outperforming the other
competent techniques with the error difference of 0.27 over XGBoost, 0.57 over ANN,
0.50 over IFA-XGBoost, 0.30 over GA-LightGBM, 0.19 over ARI-MA-LS-SVM, 0.14 over
ANN-SVM, and 0.13 over ConvLSTM. Subsequently, the AR-ERLM model attained the
MSE score of 6.01, outperforming the other existing technique XGBoost by 1.39, ANN by
3.16, IFA-XGBoost by 2.72, GA-LightGBM by 1.56, ARI-MA-LS-SVM by 1.0, ANN-SVM by
0.75, and ConvLSTM by 0.66. For k-fold 10, the AR-ERLM model attains the minimal error
of 2.70 for MAPE, exhibiting the error difference of 1.39 over XGBoost, 3.63 over ANN,
3.03 over IFA-XGBoost, 2.62 over GA-LightGBM, 1.74 over ARI-MA-LS-SVM, 0.81 over
ANN-SVM, and 0.64 over ConvLSTM. From the comparative evaluation, the AR-ERLM
model attained minimal errors for stock movement prediction due to its high potential in
capturing the non-linear relationships and trends in complex time series data. Furthermore,
the proposed approach attained low error values for the stock movement prediction and
outperformed other baseline techniques utilized for comparison.
Systems 2025, 13, 162 24 of 30
forming the other competent techniques with the error difference of 0.27 over XGBoost,
0.57 over ANN, 0.50 over IFA-XGBoost, 0.30 over GA-LightGBM, 0.19 over ARI-MA-LS-
SVM, 0.14 over ANN-SVM, and 0.13 over ConvLSTM. Subsequently, the AR-ERLM
model attained the MSE score of 6.01, outperforming the other existing technique
XGBoost by 1.39, ANN by 3.16, IFA-XGBoost by 2.72, GA-LightGBM by 1.56, ARI-MA-
LS-SVM by 1.0, ANN-SVM by 0.75, and ConvLSTM by 0.66. For k-fold 10, the AR-ERLM
model attains the minimal error of 2.70 for MAPE, exhibiting the error difference of 1.39
over XGBoost, 3.63 over ANN, 3.03 over IFA-XGBoost, 2.62 over GA-LightGBM, 1.74
over ARI-MA-LS-SVM, 0.81 over ANN-SVM, and 0.64 over ConvLSTM. From the com-
parative evaluation, the AR-ERLM model attained minimal errors for stock movement
prediction due to its high potential in capturing the non-linear relationships and trends
in complex time series data. Furthermore, the proposed approach attained low error
values for the stock movement prediction and outperformed other baseline techniques
utilized for comparison.
MAE RMSE
MAPE MSE
Figure 10. Comparative analysis of Nifty50 data using k-fold.
4.5. Comparative Discussion
Table 1 demonstrates the comparative discussion of the AR-ERLM model with the
other implemented techniques, such as GA-XGBoost, Conv-LSTM, XGBoost, ANN, and
Figure 10. Comparative analysis of Nifty50 data using k-fold.

Systems 2025,13, 162 23 of 28
4.5. Comparative Discussion
Table 1demonstrates the comparative discussion of the AR-ERLM model with the
other implemented techniques, such as GA-XGBoost, Conv-LSTM, XGBoost, ANN, and
IFA-XGBoost. Stock movement prediction has gotten tremendous attention in recent times.
However, stock prices are intrinsically complex, non-linear, and non-stationary; it is still
challenging to make reliable predictions about the direction of stock prices. The existing
methods employed for this task still face certain difficulties, such as overfitting issues,
robustness, and data availability. To tackle these issues, this research presented an AR-
ERLM model that incorporates the RNN, light GBM, and ARIMA statistical analysis. RNNs
extract relevant features from historical data without manual intervention, and the Light
GBM provides feature importance scores to aid in understanding which features contribute
most to predictions. ARIMA captures linear dependencies in time series data, making
it suitable for modeling stock prices that often exhibit trends and seasonality. Moreover,
the proposed approach effectively handles the high dimensional data, minimizes the
computation overload, extracts more significant features, and provides high prediction
performance. Table 2illustrates the comparative discussion of AR-ERLM and other existing
models using k-fold validation.
Table 1. Comparative discussion of AR-ERLM using training percentage 90.
TP 90
Dataset/Methods
Metrics XGBoost ANN IFA-
XGBoost
GA-Light
GBM
ARI-MA-
LS-SVM
ANN-
SVM
ConvLSTM
AR-ERLM
Meta Data
MAE 1.91 2.49 1.99 1.91 1.91 1.9 1.8 1.76
RMSE 2.56 3.28 2.75 2.57 2.55 2.55 2.54 2.53
MAPE 3.64 4.98 4.71 4.4 4.34 4.19 3.81 3.43
MSE 6.55 10.78 7.57 6.65 6.55 6.55 6.53 6.43
Amazon Data
MAE 1.93 2.7 1.99 1.96 1.87 1.84 1.8 1.79
RMSE 2.71 3.43 2.82 2.607 2.59 2.589 2.589 2.588
MAPE 4.68 4.16 3.96 3.91 3.49 3.36 3.13 2.81
MSE 7.36 11.8 8 6.79 6.71 6.72 6.71 6.70
Netflix Data
MAE 1.83 2.36 1.85 1.82 1.78 1.77 1.71 1.70
RMSE 2.4 2.87 2.68 2.61 2.44 2.41 2.41 2.38
MAPE 3.09 4.77 4.55 3.65 3.27 3.21 3.06 3.05
MSE 5.79 8.26 7.20 6.84 5.96 5.81 5.78 5.66
Nifty50
Data
MAE 2.27 2.53 2.30 2.18 2.05 1.90 1.87 1.82
RMSE 3.05 3.06 2.98 2.89 2.88 2.69 2.52 2.39
MAPE 4.41 7.49 6.31 4.76 4.36 4.31 3.42 2.55
MSE 9.30 9.36 8.86 8.37 8.28 7.22 6.37 5.72
Table 2. Comparative discussion of AR-ERLM using k-fold 10.
k-Fold 10
Dataset/Methods
Metrics XGBoost ANN IFA-
XGBoost
GA-Light
GBM
ARI-MA-
LS-SVM
ANN-
SVM
ConvLSTM
AR-ERLM
Meta Data
MAE 2.21 2.75 2.52 2.14 2.13 1.97 1.90 1.53
RMSE 2.83 3.41 3.19 3.13 2.89 2.81 2.47 2.43
MAPE 5.91 5.92 5.35 4.01 3.69 3.42 3.24 2.90
MSE 8.04 11.65 10.18 9.82 8.37 7.90 6.12 5.93

Systems 2025,13, 162 24 of 28
Table 2. Cont.
k-Fold 10
Dataset/Methods
Metrics XGBoost ANN IFA-
XGBoost
GA-Light
GBM
ARI-MA-
LS-SVM
ANN-
SVM
ConvLSTM
AR-ERLM
Amazon Data
MAE 1.65 2.53 2.01 2.00 1.93 1.82 1.73 1.60
RMSE 2.63 3.07 2.82 2.81 2.71 2.56 2.43 2.42
MAPE 3.57 4.86 4.52 4.17 3.87 3.36 3.22 3.06
MSE 6.91 9.42 7.96 7.91 7.36 6.57 5.88 5.88
Netflix Data
MAE 1.44 2.41 2.08 2.00 1.68 1.67 1.42 1.38
RMSE 2.4 2.87 2.68 2.61 2.44 2.41 2.41 2.38
MAPE 3.11 5.89 5.41 5.16 4.13 4.00 3.48 2.98
MSE 2.36 3.00 2.97 2.71 2.66 2.50 2.35 2.34
Nifty50
Data
MAE 1.87 2.19 2.19 2.03 2.00 1.91 1.87 1.80
RMSE 2.47 2.85 2.84 2.71 2.70 2.58 2.52 2.45
MAPE 3.60 7.36 6.42 5.41 4.45 4.37 3.84 3.17
MSE 6.09 8.13 8.07 7.34 7.30 6.66 6.35 6.01
4.6. Ablation Study
The ablation study is carried out to examine the contribution of different components,
including the ARIMA, RNN, and LightGBM, to the improvement of the AR-ERLM model.
Further, the performance of the AR-ERLM and the individual models is examined, and
the results are depicted in Figure 11. From Figure 11, the proposed AR-ERLM model
achieved the minimum MSE score of 6.70, which is lower than ARIMA by 1.26, RNN by
1.55, and LightGBM by 3.83. More specifically, the proposed AR-ERLM model integrates
the advantages of ARIMA, RNN, and Light GBM model and reduces the error in the
prediction. In addition, the proposed model combines the ARIMA, RNN, and Light GBM
and excels in identifying linear correlations and trends in time series data. Specifically,
the RNN assists in learning the sequential data because of the internal memory, which
makes the model appropriate for identifying patterns across time. Further, this observation
explicates that the AR-ERLM possesses greater potential to predict the stock movement
price compared to other individual models. Moreover, the ablation study analyzes the
contribution of different components, including the ARIMA, RNN, and LightGBM, in the
AR-ERLM model for improving stock movement prediction.
Systems 2025, 13, 162 26 of 30
MAPE 3.11 5.89 5.41 5.16 4.13 4.00 3.48 2.98
MSE 2.36 3.00 2.97 2.71 2.66 2.50 2.35 2.34
Nifty50
Data
MAE 1.87 2.19 2.19 2.03 2.00 1.91 1.87 1.80
RMSE 2.47 2.85 2.84 2.71 2.70 2.58 2.52 2.45
MAPE 3.60 7.36 6.42 5.41 4.45 4.37 3.84 3.17
MSE 6.09 8.13 8.07 7.34 7.30 6.66 6.35 6.01
4.6. Ablation Study
The ablation study is carried out to examine the contribution of different compo-
nents, including the ARIMA, RNN, and LightGBM, to the improvement of the AR-
ERLM model. Further, the performance of the AR-ERLM and the individual models is
examined, and the results are depicted in Figure 11. From Figure 11, the proposed AR-
ERLM model achieved the minimum MSE score of 6.70, which is lower than ARIMA by
1.26, RNN by 1.55, and LightGBM by 3.83. More specifically, the proposed AR-ERLM
model integrates the advantages of ARIMA, RNN, and Light GBM model and reduces
the error in the prediction. In addition, the proposed model combines the ARIMA, RNN,
and Light GBM and excels in identifying linear correlations and trends in time series da-
ta. Specifically, the RNN assists in learning the sequential data because of the internal
memory, which makes the model appropriate for identifying patterns across time. Fur-
ther, this observation explicates that the AR-ERLM possesses greater potential to predict
the stock movement price compared to other individual models. Moreover, the ablation
study analyzes the contribution of different components, including the ARIMA, RNN,
and LightGBM, in the AR-ERLM model for improving stock movement prediction.
Figure 11. Ablation study.
4.7. Diebold–Mariano Test
In this research, the Diebold–Mariano (DM) test is conducted to evaluate the predic-
tive ability of different prediction models concerning their prediction error sequences.
With the application of a series of statistical tests, the DM test assesses whether there is a
substantial difference in the prediction capacity of the models under examination. Be-
Figure 11. Ablation study.

Systems 2025,13, 162 25 of 28
4.7. Diebold–Mariano Test
In this research, the Diebold–Mariano (DM) test is conducted to evaluate the predictive
ability of different prediction models concerning their prediction error sequences. With the
application of a series of statistical tests, the DM test assesses whether there is a substantial
difference in the prediction capacity of the models under examination. Because of this,
the DM test serves as an effective tool to assess the efficiency of various stock movement
forecasting models prediction in the future. Further, the DM test to assess the performance
is expressed as follows:
DM12 =D12
σD12
(25)
D12 =1
P
P
∑
i=1e(1)
it+12−e(2)
it+12(26)
where
P
indicates the stock index price,
D12
denotes the out-of-sample difference in the
MSE between two prediction models,
D12
indicates the mean of
D12
, and
σD12
represents the
standard deviation of
D12
. Further,
e(1)
it+12
and
e(2)
it+12
represent the prediction errors of
the two prediction models for flow I respectively. When the value of
DM
is less than 0, it
indicates that model 1 carries out the prediction better than model 2. Table 3depicts the
Diebold–Mariano test carried out for the different models utilized in the prediction.
Table 3. Diebold–Mariano test.
Model ARIMA RNN LightGBM
ARIMA - −0.854 −7.346
RNN 0.000 - −8.976
LightGBM 0.000 −0.275 -
4.8. Statistical Results
The statistical results obtained with the stock data and the Technical indicators for the
Nifty50 data points are shown in Table 4. Further, the statistical test is carried out to find
the significant difference between the data points and ensure the robustness of the results.
Table 4. Statistical results.
S. No Stock Data Technical Indicators
Best Mean Variance Best Mean Variance
1 82,100 16,436.41
7.32
×
10
882,100 5292.3
2.05
×
10
8
2 77,700 15,813.91
6.51
×
10
877,700 5155.382
1.84
×
10
8
3 84,500 16,794.48
7.77
×
10
884,500 5377.683
2.16
×
10
8
4 101,900 19,326.21
1.15
×
10
9101,900 5937.903
3.12
×
10
8
5 118,200 21,685.12
1.57
×
10
9118,200 6455.745
4.18
×
10
8
6 172,800 29,384.55
3.44
×
10
9172,800 8134.185
8.89
×
10
8
7 164,100 28,076.77 3.1 ×109164,100 7843.107
8.02
×
10
8
8 143,800 25,233.83
2.36
×
10
9143,800 7223.883
6.16
×
10
8
9 148,000 25,866.29 2.5 ×109148,000 7621.368
6.51
×
10
8
10 103,200 19,484.65
1.18
×
10
9103,200 6227.626
3.18
×
10
8

Systems 2025,13, 162 26 of 28
Table 4. Cont.
S. No Stock Data Technical Indicators
Best Mean Variance Best Mean Variance
11 129,600 23,267.16 1.9 ×109129,600 7055.614 5×108
12 146,100 25,606.84
2.43
×
10
9146,100 7402.419
6.36
×
10
8
13 232,100 37,989.47
6.29
×
10
9232,100 10,115.53
1.61
×
10
9
14 176,000 30,000.12
3.57
×
10
9176,000 8373.068
9.22
×
10
8
15 125,400 22,800.46
1.77
×
10
9125,400 6807.859
4.69
×
10
8
16 158,700 27,607.59
2.88
×
10
9158,700 7873.989 7.5 ×108
17 185,900 31,540.09
3.99
×
10
9185,900 8734.912
1.03
×
10
9
18 175,500 30,072.63
3.54
×
10
9175,500 8421.444
9.17
×
10
8
19 191,200 32,360.76
4.22
×
10
9191,200 8940.341
1.09
×
10
9
20 192,000 32,504.62
4.25
×
10
9192,000 8983.887 1.1 ×109
21 185,100 31,539.45
3.95
×
10
9185,100 8784.664
1.02
×
10
9
22 256,300 41,711.68
7.69
×
10
9256,300 11,016.64
1.96
×
10
9
23 267,300 43,268.17
8.38
×
10
9267,300 11,360.65
2.13
×
10
9
24 210,100 35,041.69
5.12
×
10
9210,100 9570.6
1.31
×
10
9
25 208,700 34,834.81
5.05
×
10
9208,700 9535.426 1.3 ×109
5. Conclusions
In conclusion, this research proposes an ensemble method that leverages the benefits
of the statistical analysis model with the RNN and LightGBM. Stock market predictions
always carry inherent uncertainty, and combining multiple models can provide a more
robust approach to forecasting. By using the proposed AR-ERLM model, traders can
make informed decisions about buying or selling stocks. Furthermore, the proposed
model is computationally efficient and can handle large datasets with minimal memory
usage. It also combines the strengths of decision trees and gradient boosting, resulting
in accurate predictions. Additionally, the technical indicators employed in this research
aid in determining the direction of trends and provide more statistical parameters for
evaluation. The performance of the AR-ERLM model for stock movement prediction is
compared with other implemented methods, and the outcomes show that the proposed
framework achieves lower errors with MSE 4.45, RMSE 2.35, and MAE 1.58. Moreover,
the implementation results ensure the practical application of the AR-ERLM model for
predicting stock price movement and offer investors greater decision support to adjust their
investment strategies for maximizing profit and lowering the risks associated with margin
trading. Even though most of the stock prices have a daily pattern, as in the proposed
approach, this can be changed in other areas due to the seasonal pattern on some sales
datasets. Hence, an attempt will be made to utilize diverse lengths of historical data and
other significant features, including the exchange rates and other macroeconomic indicators
in the future.
Author Contributions: Writing—original draft preparation, A.A. (Adel Alarbi); supervision, W.K.;
project administration, A.A. (Ahmad Alzubi) All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.

Systems 2025,13, 162 27 of 28
Data Availability Statement: The data that support the findings of this study are available online:
the Amazon dataset: https://finance.yahoo.com/quote/AMZN, which was accessed on 2 May 2024.
Meta dataset: https://finance.yahoo.com/quote/META accessed on 2 May 2024. Netflix dataset:
https://finance.yahoo.com/quote/NFLX accessed on 2 May 2024.
Conflicts of Interest: The authors declare no conflicts of interest.
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