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MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue II, February 2025

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Performance Evaluation of Long Short-Term Memory and

Autoregressive Integrated Moving Average Time Series Models for

Stock Price Prediction

Adeniran, Rachel Ihunanya., Olabiyisi, Stephen Olatunde., Ismaila, Wasiu Oladimeji., Oyedele, Adebayo Olalere.,

Olagbemiro, Catherine Olatorera

Department of Computer Science Ladoke Akintola University of Technology, Ogbomoso, Oyo state Nigeria

DOI : https://doi.org/10.51583/IJLTEMAS.2025.14020021

Received: 01 March 2025; Accepted: 05 March 2025; Published: 15 March 2025

Abstract: Stock price prediction is a critical task in financial markets, often complicated by the challenges of modeling highly

volatile, non-linear, and dynamic time series data. This study evaluates the performance of two prominent forecasting models:

Long Short-Term Memory (LSTM) networks, known for their ability to capture long-term dependencies and non-linear patterns,

and the Auto-Regressive Integrated Moving Average (ARIMA), a traditional statistical model adept at linear trend modeling.

Historical stock price data from the Nigerian Exchange Limited (NGX) was utilized. Both models were implemented in a Python

environment, and their predictive accuracy was assessed using performance metrics, including Mean Absolute Error (MAE), Root

Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and R-squared (R²). Additionally, the Diebold-Mariano

(DM) test was employed to statistically compare the models’ predictive accuracies.

This study highlights the potential of LSTM models for robust stock price forecasting and provides valuable insights for selecting

predictive models based on data complexity and market dynamics.

Key word: Performance, Evaluation, Stock Price, LSTM, ARIMA.

I. Introduction

Predicting the future direction of stock prices is an interesting research quest for both researchers and investors in the stock

market. Due to many reasons, it is difficult to predict future stock market price behavior accurately. There is significant research

addressing this challenge with a variety of approaches aimed at predicting future stock market price behavior (Appel, 2005;

Brown et al., 1998; El-Nagar et al., 2022; and Fromlet, 2001). A prevalent approach in predicting stock prices involves applying

machine learning algorithms to learn from historical price data, thereby enabling future price predictions. These models

demonstrate predictive power on historical stock price data, outperforming traditional methods due to their suitability for this data

type. Recurrent neural networks, such as Long Short-Term Memory (LSTM) networks, exhibit short-term memory, a feature that

can be beneficial in improving prediction results compared to more conventional methods (Nelson et al., 2017).

Given the nature of short-term predictive analysis based on time series data, the combination of machine learning and technical

analysis in forecasting stock prices is widely applied. Some studies suggest that stock price technical analysis patterns aim to

detect stock volatility patterns, which can help investors maximize returns. Consequently, different stock price and technical

analysis indicators have been proposed, including Bollinger Bands, Moving Average Convergence Divergence (MACD), Relative

Strength Index (RSI), Moving Average (MA), Stochastic Momentum (SM), and Meta Sine Wave (MSW). Additionally, well-

known stock price movement patterns, such as head and shoulders, triangles, flags, Fibonacci fans, and Andrew’s pitchfork, are

recognized as valuable indicators for investment decisions (Nelson et al., 2017; Borovkova and Tsiamas, 2019). These

perspectives provide investors with more effective tools for making informed investment decisions.

Alternative techniques for analyzing time series data include the Difference-in-Differences (DID) method, as discussed in the

study of Trinh et al., (2021), and the non-linear autoregressive distributed lag approach of Le et al., (2022).

Advancements in time series analysis, particularly deep learning models like Long Short-Term Memory (LSTM) networks and

statistical models like Autoregressive Integrated Moving Average (ARIMA), have demonstrated significant potentials in

enhancing stock price forecasting accuracy. However, there remains a need for a comprehensive performance evaluation of these

models to determine their effectiveness in different market conditions and data patterns.

In the quest to contribute to knowledge, this study aims to explore the potentials of time series models (LSTM and ARIMA) to

identify trends and potentially forecast future stock prices based on historical data movements with the objectives to;

i. implement Long-Short Term Memory and Autoregressive Integrated Moving Average time series models to predict

Nigerian stock prices using the dataset from Nigerian Exchange Limited (NGX)

ii. evaluate the accuracy and effectiveness of the prediction models using Mean Squared Error (MSE), Mean Absolute

Percentage Error (MAPE), Root Mean Squared Error (RMSE) and R-squared (R

) as performance metrics.

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

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iii. statistically analyze Long-Short Term Memory and Autoregressive Integrated Moving Average time series models using

Diebold-Mariano test.

II. Literature Review

Several works have been done to proffer reliable solutions to challenges facing the predictability of equity stock movements to

enable a typical investor to make informed decisions. These informed decisions in turn give the investor the leverage to create

wealth. Some works or studies done by scholars ranging from the application of conventional statistical and analytical tools to the

modern-day application of Artificial intelligence (machine learning and advanced neural networks) models and techniques were

highlighted as follows:

Adetunji et al., (2013) highlighted the comparative strengths of Artificial Neural Networks (ANN) and Bayesian Networks (BN)

for stock forecasting. Their findings indicated that Bayesian Networks, leveraging conditional probability tables, offered a faster

and more efficient solution, particularly when data availability was limited. In contrast, ANN required larger training datasets and

significant computational resources, achieving a predictive accuracy of 59.38% compared to 78.13% for Bayesian Networks.

These results underscore the importance of considering data characteristics and context when selecting forecasting tools.

In Abubakar and Adeboye (2014), the equity market's significance in the investment world cannot be over-emphasized. The

increment or decrement shift in stock price trends can influence the decision-making disposition of a typical investor. In the early

years of stock market forecasting, predicting models deployed are seemingly linear. However, recent studies have shown an

increase in the use of deep learning techniques for the prediction of stock market returns. In this study, two deep learning

architectures (RNN and LSTM) were deployed as models for the forecasting of Indian national stock exchange listed companies.

The result showed commendable performance of the deep learning hybrid models deployed. The long short-term memory model

performance accuracy was outstanding.

Adebiyi et al., (2012) opined that Stock market prediction is mostly characterized using technical indices alone, however, in their

study, they chose to deviate away from the conventional norm by applying machine learning methods (Top-Level Random Forest

(TRF), Logistic Regression (LR), Support Vector Machine (SVM) and Neural networks (NN) on equity stock trading. The

experimental study outcome shows TRF prediction was more accurate in performance than other algorithms tested.

Stock market investment is of great economic importance to individuals and the world at large. However, its volatile uncertainties

need efficient forecasting tools. Godknows and Olusanya, (2014) carried out a study on stock price prediction using RNN by

collecting Google stock price dataset of over ten years. The model built indicated RNN can predict the future stock price returns

correctly in short term basis.

Ibidapo et al., (2017) showed financial time series related problems, forecasting future equity stock values and returns needs

robust mathematical or technological models and tools. This is due to the non-linear nature of financial time series challenges and

its attendant volatility and uncertainties. The challenges posed by the complexity of equity stocks have drawn the attention or

interest of researchers, investors, and academia community. Ibidapo et al., (2017) carried out a study on Brazilian national stock

prices by evaluating the performance predictability of LSTM neural network. The results shown LSTM predicted accurately the

future stock movement returns of selected equity stocks under test.

Equity Share Market investment entails monitoring and managing investment risks, and not attempting to evade it. With the

above mindset Chanddrika and Sreenvasan, (2020), a passionate knowledgeable investor would be wise enough to seek effective

predicting tools with high accuracy that can help with informed decision for analyses and deduction on what stock to buy or sell

or to hold until later time in the future. Chanddrika and Sreenvasan (2020) combined technical analysis and machine learning

architecture to predict the performance of the hybrid tools used on stocks datasets. The result showed the hybrid models proposed

did well in the forecast exercise.

Adetunji et al., (2013) proposed combining technical and fundamental factors for ANN-based models to address limitations in

predictive capability. They also suggested exploring hybrid frameworks that integrate ANN and BN to leverage the strengths of

both models. Such a hybrid approach could mitigate the shortcomings of individual methods, offering more reliable predictions

for complex, emerging markets like Nigeria's. This perspective aligns with broader research trends advocating for

multidisciplinary approaches in financial forecasting

Having evaluated the non-linearity nature of financial market, (both commodities and stock market) Neenwi et al., (2013)

proposed the use of RNN model to tackle the challenge of predicting accurately (via relevant datasets) the future values of stock

market. The RNN model built was trained, validated, and tested using NSE stock prices, result revealed via the graphs plotted and

obtained showed that the recurrent neural network variant predicted accurately the future price returns of selected equities.

Using the Long Short-Term Memory (LSTM) algorithm and the corresponding technical analysis indicators such as Simple

Moving Average (SMA), Convergence Divergence Moving Average (MACD) and Relative Strength Index as done by Phouc et

al., (2024) produced a result that showed the forecasting model has a high accuracy of about 93% for most of the stock data used,

demonstrating the appropriateness of the LSTM model.

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Critically studying the work of Adebola et al., (2024), which had over 90% accuracy in its result, the research used the LSTM

model with some performance metrics to predict future stock market prices. This work went further to suggest that further

research can be explored by combining the LSTM model with other models in order to increase the accuracy level of the

prediction.

Long Short-Term Memory

Long Short-Term Memory is a type of RNN Recurrent Neural Network that can retain long-term dependencies in sequential data.

LSTMs are able to process and analyze sequential data, such as time series, text, and speech. LSTMs can be particularly powerful

for complex patterns.

LSTMs use a series of 'gates' which control how the information in a sequence of data comes into, is stored in and leaves the

network. There are three gates in a typical LSTM; forget gate, input gate and output gate. These gates can be thought of as filters

and are each their own neural network. Unlike traditional neural networks, LSTM incorporates feedback connections,

allowing it to process entire sequences of data, not just individual data points. This makes it highly effective in

understanding and predicting patterns in sequential data like time series, text, and speech. LSTM has become a powerful

tool in artificial intelligence and deep learning, enabling breakthroughs in various fields by uncovering valuable insights

from sequential data.

LSTMs are predominantly used to learn, process, and classify sequential data because these networks can learn long-term

dependencies between time steps of data. Common LSTM applications include stock market prediction, sentiment analysis,

language modeling, speech recognition, and video analysis. LSTMs are employed to analyze time series data, like stock prices, by

learning patterns and making predictions. In particular, the LSTM algorithm (Long Short- Term Memory) confirms the stability

and efficiency in short-term stock price forecasting than other models. LSTM cells are used in recurrent neural networks that

learn to predict the future from sequences of variable lengths. Note that recurrent neural networks work with any kind of

sequential data.

Autoregressive Integrated Moving Average

ARIMA (Autoregressive Integrated Moving Average)

A famous and widely used forecasting method for time-series prediction is the AutoRegressive Integrated Moving Average

(ARIMA) model. This model captures trends, seasonality and random noise in the data. They are powerful for forecasting stock

market trends by analyzing historical data and identifying potential future price movements. The performance of the ARIMA

model can be evaluated using metrics like Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Meat Squared Error

(RMSE), and Mean Absolute Percentage Error (MAPE), ensuring high accuracy in stock price predictions. In an Autoregressive

model, the forecasts correspond to a linear combination of past values of the variable.

Although ARIMA models can be highly accurate and reliable under the appropriate conditions and data availability, one of the

key limitations of the model is that the parameters need to be manually defined; therefore, finding the most accurate fit can be a

long trial-and-error process. ARIMA models are not explicitly designed to capture seasonal patterns in the data, which can lead to

inaccuracies in forecasting for datasets with significant seasonal variations. It is used in technical analysis to predict an asset's

future performance. ARIMA modeling is generally inadequate for long-term forecasting, such as more than six months ahead,

because it uses past data and parameters that are influenced by human thinking.

III. Methodology

The research employed advanced time series analysis techniques to explore the potentials of predictive models for stock price

forecasting. Historical stock price data was analyzed to identify patterns and trends, providing a foundation for implementing

Long Short-Term Memory (LSTM) and AutoRegressive Integrated Moving Average (ARIMA) models. LSTM, implemented

using TensorFlow and Keras, captured long-term dependencies, while ARIMA, built with the Statsmodels library, utilized

statistical properties for forecasting. Data preprocessing, including cleaning and normalization, ensured the accuracy of the

models, which were trained on separate training and validation sets. Evaluation metrics such as Mean Absolute Error (MAE),

Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE)and R-squared (R

), as well as Diebold-Mariano

statistical test measured the models' accuracy and effectiveness, enabling comparative analysis. The approach was structured to

align with the aim and objectives of the study, offering insights into the strengths and limitations of time series models for stock

price prediction.

These were achieved through these processes:

i. Data Collection: Stock price data was acquired from Nigerian Exchange Limited (NGX) for the period from January

2015 to December 2019.

ii. Data Preprocessing: The acquired dataset was cleaned, normalized, feature engineered and split into training which

comprises 80% of the data and testing sets which is 20%.

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iii. Model Implementation: The Long-Short Term Memory and Autoregressive Integrated Moving Average time series

models were implemented.

iv. Model Evaluation: The evaluation metrics Mean Absolute Error, Root Mean Squared Error, Mean Absolute Percentage

Error and R-squared were used to evaluate the performance of these time series models.

v. Statistical Analysis: Statistically analyzed the performance of LSTM and ARIMA models using Diebold-Mariano (DM)

test for more insight.

IV. Results and Discussions

The LSTM model showcased its ability to accurately predict stock prices by effectively learning from historical data and adapting

to both long-term trends and short-term fluctuations. Its use of memory cells and capacity to process non-linear relationships

enables it to handle complex financial data and volatile market conditions with greater accuracy. On the other hand, the ARIMA

model proved more suitable for linear and stationary datasets, performing well in stable conditions but struggling with the non-

linearities and abrupt changes inherent in stock price movements. While ARIMA relies on statistical assumptions that limit its

flexibility, LSTM demonstrates superior predictive power for dynamic and unpredictable time series.

LSTM Model Predictions

The LSTM model demonstrated a remarkable ability to predict stock prices by capturing both long-term trends and short-term

fluctuations as shown in figure 1. Unlike traditional models, which may struggle to adapt to the volatility in financial data, LSTM

was able to learn from past sequences and use that knowledge to forecast future values. This capability is particularly important in

stock price prediction, where patterns are not only influenced by long-term market trends but also by sudden changes driven by

external factors. The model's structure, which includes memory cells to retain information over time, enables it to handle these

complex dynamics effectively. By learning from sequences of past data, LSTM provides more accurate forecasts, even when the

data exhibits erratic behavior. This makes it a powerful tool for applications in time series forecasting, where accuracy in

predicting both trends and variations is critical.

The LSTM model excels at modelling time-dependent data, particularly in financial markets where prices are influenced by

numerous dynamic and interrelated factors. In stock price prediction, the ability to understand both the long-term trend and short-

term deviations is crucial, and LSTM’s memory mechanism allows it to effectively balance these two aspects. The model not only

predicts the general direction of the price movement but also anticipates sudden price spikes or drops with a higher degree of

accuracy. This is in stark contrast to simpler models, which may be able to predict general trends but fail to capture the nuances of

sudden market shifts.

The enhanced predictive power of LSTM can offer investors and analysts a valuable tool for making informed decisions in an

unpredictable market. As a result, the LSTM model stands out as a more reliable and efficient approach for time series forecasting

in complex domains like stock price prediction.

Fig. 1: LSTM Model Prediction Train Result

The ARIMA Model Prediction

The ARIMA model is well-suited for linear and stationary data, making it effective for time series that follow consistent patterns.

As shown in Figure 2. It operates by modeling the differences in the series to achieve stationarity, which is a key requirement for

the model's performance. In cases where stock prices exhibit stable trends over time, ARIMA can provide reliable predictions.

However, its performance tends to deteriorate when faced with more complex, non-linear data, such as stock prices, which are

influenced by various unpredictable factors.

While ARIMA can handle simple, stationary data with a clear trend or seasonality, it struggles with non-linear relationships.

Stock prices often experience fluctuations driven by external events, market sentiment, and other factors that are not easily

captured by the model’s assumptions. ARIMA's reliance on statistical assumptions, such as the need for stationarity, limits its

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ability to adapt to such complexities. This makes it less effective in scenarios where the data exhibits volatility or structural

breaks.

The ARIMA model's major limitation lies in its inability to adapt to dynamic, non-linear datasets like stock prices. While it

performs well in predicting relatively stable, linear time series, it fails to capture the intricate and often unpredictable nature of

financial markets. Moreover, ARIMA's dependency on pre-determined parameters and its assumption of linearity restrict its

flexibility. As financial data is typically non-linear, this creates a gap in ARIMA's practical application for stock price

forecasting. Therefore, for more accurate predictions in volatile markets, alternative models that can account for non-linearities,

such as LSTM, are often preferred. Despite these drawbacks, ARIMA remains a useful tool for simpler time series analysis.

Fig. 2: ARIMA Model Price Prediction

Performance Evaluations of Both Models.

The performance comparison of the LSTM and ARIMA models highlights the superiority of LSTM in predicting stock prices.

Based on the evaluation metrics, the LSTM model consistently outperformed ARIMA across all criteria. As shown in table 4.3.

LSTM achieved a lower Mean Absolute Error (MAE) of 3.78 compared to ARIMA's 5.12, indicating higher accuracy in its

predictions. Similarly, LSTM recorded a lower Root Mean Squared Error (RMSE) of 4.89 against ARIMA's 6.34, further

underscoring its precision.

In terms of Mean Absolute Percentage Error (MAPE), LSTM showed a smaller error margin at 3.15%, while ARIMA lagged

with 4.24%. Additionally as shown in Figure 3 bar graph and Figure 1 trend graph respectively, the R-squared (R²) value for

LSTM was 0.91, demonstrating better explanatory power, whereas ARIMA achieved a lower R² of 0.820, affirming LSTM's

overall superior performance

Table 1: Model Performance Comparison

Metric

LSTM

ARIMA

MAE

3.78

5.12

RMSE

4.89

6.34

MAPE (%)

3.15

4.24

R²

0.91

0.820

Fig. 3: Model Performance Comparison Bar Graph

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Fig. 4: Model Performance Comparison Trend Graph

V. Result of the Statistical Analysis

The Diebold-Mariano (DM) test was performed to statistically compare the predictive accuracy of ARIMA and LSTM models in

forecasting stock prices. The results as shown in figure 5 And Table 2 below. The mean loss differential of −1.3715-

1.3715−1.3715, indicating that LSTM consistently produces smaller squared forecast errors than ARIMA. The DM statistic of

−6.6822-6.6822−6.6822 and a highly significant p-value of 0.0000020.0000020.000002 provide strong evidence that the

difference in performance between the models is not due to chance. This underscores LSTM's superior ability to capture non-

linear patterns and handle stock market volatility, compared to ARIMA’s limitations with such complexities. Overall, the DM test

reaffirms the earlier findings, demonstrating LSTM's effectiveness as a more accurate predictive tool for stock price forecasting.

The statistical analysis revealed key insights from the data. As shown in Figure 6 below. The probability density function (PDF)

indicated a bimodal distribution, with prominent peaks around 0.25 and 0.5, suggesting the presence of two distinct groups within

the dataset. The tails of the density curve extended slightly, highlighting the potential for outliers or low-density regions. As

shown in Figure 7 below. The autocorrelation function (ACF) demonstrated significant correlations across lags up to

approximately 30, indicating strong dependence on past values. Meanwhile, the partial autocorrelation function (PACF) exhibited

significant spikes at lags 1 and 2, with values diminishing to near zero for higher lags, suggesting that the time series was well-

suited for a second-order autoregressive (AR(2)) model. Overall, the analysis provided evidence of a structured distribution and

time-dependent patterns, laying a foundation for further modeling and interpretation.

FIG.5: Diebold-Mariano Loss Differential between ARIMA and LSTM forecasts

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Fig.6: Density statistical result

Table 2: Diebold-Mariano Test Results

Metric

Value

Mean Loss Differential

-1.3715

Variance of loss

0.0421

Diebold-Mariano test

-6.6822

P-value

0.000002

Fig.7: Autocorrelation (ACF) and Partial Autocorrelation (PACF) statistical result

VI. Conclusion

This study explored the potential of time series models, specifically ARIMA and LSTM, to identify trends and forecast stock

prices based on historical data. The research aimed to provide a robust framework for understanding stock price movements and

improve the accuracy of stock price predictions. Historical stock data from Yahoo Finance served as the foundation for analysis,

with comprehensive preprocessing techniques such as data cleaning, normalization, and feature engineering ensuring high-quality

datasets for modelling.

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The ARIMA model, known for its simplicity and ability to model linear relationships, demonstrated effectiveness in capturing

short-term dependencies in stock prices. However, its limitations became evident when dealing with non-linear relationships and

complex seasonal patterns. Conversely, the LSTM model, a deep learning-based approach, excelled in identifying long-term

dependencies and capturing intricate patterns in sequential data. Despite its advantages, LSTM required more computational

resources and was prone to overfitting, particularly when working with limited data.

Evaluation of the models revealed that LSTM outperformed ARIMA in terms of accuracy, as measured by metrics such as Mean

Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). However, the

comparative analysis also highlighted the significance of balancing model complexity with interpretability, as ARIMA offered

greater simplicity and ease of deployment. The research further acknowledged the influence of external factors, such as news

events and macroeconomic conditions, which were beyond the scope of the models but essential for comprehensive stock price

forecasting.

In conclusion, the study demonstrated the applicability of ARIMA and LSTM models for stock price forecasting while

emphasizing the need for hybrid approaches and integration of external data sources to enhance prediction accuracy and

reliability.

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