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22 pages, 828 KB  
Article
Stock Price Prediction Using FinBERT-Enhanced Sentiment with SHAP Explainability and Differential Privacy
by Linyan Ruan and Haiwei Jiang
Mathematics 2025, 13(17), 2747; https://doi.org/10.3390/math13172747 - 26 Aug 2025
Viewed by 622
Abstract
Stock price forecasting remains a central challenge in financial modeling due to the non-stationarity, noise, and high dimensionality of market dynamics, as well as the growing importance of unstructured textual information. In this work, we propose a multimodal prediction framework that combines FinBERT-based [...] Read more.
Stock price forecasting remains a central challenge in financial modeling due to the non-stationarity, noise, and high dimensionality of market dynamics, as well as the growing importance of unstructured textual information. In this work, we propose a multimodal prediction framework that combines FinBERT-based financial sentiment extraction with technical and statistical indicators to forecast short-term stock price movement. Contextual sentiment signals are derived from financial news headlines using FinBERT, a domain-specific transformer model fine-tuned on annotated financial text. These signals are aggregated and fused with price- and volatility-based features, forming the input to a gradient-boosted decision tree classifier (XGBoost). To ensure interpretability, we employ SHAP (SHapley Additive exPlanations), which decomposes each prediction into additive feature attributions while satisfying game-theoretic fairness axioms. In addition, we integrate differential privacy into the training pipeline to ensure robustness against membership inference attacks and protect proprietary or client-sensitive data. Empirical evaluations across multiple S&P 500 equities from 2018–2023 demonstrate that our FinBERT-enhanced model consistently outperforms both technical-only and lexicon-based sentiment baselines in terms of AUC, F1-score, and simulated trading profitability. SHAP analysis confirms that FinBERT-derived features rank among the most influential predictors. Our findings highlight the complementary value of domain-specific NLP and privacy-preserving machine learning in financial forecasting, offering a principled, interpretable, and deployable solution for real-world quantitative finance applications. Full article
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40 pages, 2222 KB  
Article
AI and Financial Fragility: A Framework for Measuring Systemic Risk in Deployment of Generative AI for Stock Price Predictions
by Miranda McClellan
J. Risk Financial Manag. 2025, 18(9), 475; https://doi.org/10.3390/jrfm18090475 - 26 Aug 2025
Viewed by 931
Abstract
In a few years, most investment firms will deploy Generative AI (GenAI) and large language models (LLMs) for reduced-cost stock trading decisions. If GenAI-run investment decisions from most firms are heavily coordinated, they could all give a “sell” signal simultaneously, triggering market crashes. [...] Read more.
In a few years, most investment firms will deploy Generative AI (GenAI) and large language models (LLMs) for reduced-cost stock trading decisions. If GenAI-run investment decisions from most firms are heavily coordinated, they could all give a “sell” signal simultaneously, triggering market crashes. Likewise, simultaneous “buy” signals from GenAI-run investment decisions could cause market bubbles with algorithmically inflated prices. In this way, coordinated actions from LLMs introduce systemic risk into the global financial system. Existing risk analysis for GenAI focuses on endogenous risk from model performance. In comparison, exogenous risk from external factors like macroeconomic changes, natural disasters, or sudden regulatory changes, is understudied. This research fills the gap by creating a framework for measuring exogenous (systemic) risk from LLMs acting in the stock trading system. This research develops a concrete, quantitative framework to understand the systemic risk brought by using GenAI in stock investment by measuring the covariance between LLM stock price predictions across three industries (technology, automobiles, and communications) produced by eight large language models developed across the United States, Europe, and China. This paper also identifies potential data-driven technical, cultural, and regulatory mechanisms for governing AI to prevent negative financial and societal consequences. Full article
(This article belongs to the Special Issue Investment Management in the Age of AI)
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36 pages, 1871 KB  
Article
Sentiment-Driven Statistical Modelling of Stock Returns over Weekends
by Pablo Kowalski Kutz and Roman N. Makarov
Computation 2025, 13(8), 201; https://doi.org/10.3390/computation13080201 - 21 Aug 2025
Viewed by 645
Abstract
We propose a two-stage statistical learning framework to investigate how financial news headlines posted over weekends affect stock returns. In the first stage, Natural Language Processing (NLP) techniques are used to extract sentiment features from news headlines, including FinBERT sentiment scores and Impact [...] Read more.
We propose a two-stage statistical learning framework to investigate how financial news headlines posted over weekends affect stock returns. In the first stage, Natural Language Processing (NLP) techniques are used to extract sentiment features from news headlines, including FinBERT sentiment scores and Impact Probabilities derived from Logistic Regression models (Binomial, Multinomial, and Bayesian). These Impact Probabilities estimate the likelihood that a given headline influences the stock’s opening price on the following trading day. In the second stage, we predict over-weekend log returns using various sets of covariates: sentiment-based features, traditional financial indicators (e.g., trading volumes, past returns), and headline counts. We evaluate multiple statistical learning algorithms—including Linear Regression, Polynomial Regression, Random Forests, and Support Vector Machines—using cross-validation and two performance metrics. Our framework is demonstrated using financial news from MarketWatch and stock data for Apple Inc. (AAPL) from 2014 to 2023. The results show that incorporating sentiment features, particularly Impact Probabilities, improves predictive accuracy. This approach offers a robust way to quantify and model the influence of qualitative financial information on stock performance, especially in contexts where markets are closed but news continues to develop. Full article
(This article belongs to the Section Computational Social Science)
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17 pages, 3264 KB  
Article
Hybrid CNN-LSTM-GNN Neural Network for A-Share Stock Prediction
by Junhao Dong and Shi Liang
Entropy 2025, 27(8), 881; https://doi.org/10.3390/e27080881 - 20 Aug 2025
Viewed by 862
Abstract
Optimization of stock selection strategies has been a topic of interest in finance. Although deep learning models have demonstrated superior performance over traditional methods, there are still shortcomings. For example, previous studies do not provide enough explanation for feature selection and usually use [...] Read more.
Optimization of stock selection strategies has been a topic of interest in finance. Although deep learning models have demonstrated superior performance over traditional methods, there are still shortcomings. For example, previous studies do not provide enough explanation for feature selection and usually use features such as closing price directly to make predictions; for example, most studies predict the trend of multiple stock indices or only individual stocks, which is difficult to be directly applied to actual stock selection. In this paper, a multivariate hybrid neural network model CNN-LSTM-GNN (CLGNN) for stock prediction is proposed, in which the CNN and the LSTM modules analyze the local and the whole, respectively, while the multivariate time series GNN module is added to explore the potential relationships between the data through the graph learning, graph convolutional, and temporal convolutional layers. CLGNN analyzes the potential relationships between the data based on the returns to classify stocks, and then develops a stock selection strategy, and directly outputs the returns and stock codes. In this paper, a hybrid filter approach based on entropy and Pearson correlation is proposed for feature selection, and experiments are conducted on all stocks in the CSI All Share Index (CSI); the results show that among multiple models, the returns obtained when the features of daily return, turnover rate, relative strength index, volume, and forward adjusted closing price are used as inputs are all the highest, and the return obtained by CLGNN is even higher than that of the other models (e.g., TCN, Transformer, etc.). Full article
(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)
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27 pages, 1363 KB  
Article
FSTGAT: Financial Spatio-Temporal Graph Attention Network for Non-Stationary Financial Systems and Its Application in Stock Price Prediction
by Ze-Lin Wei, Hong-Yu An, Yao Yao, Wei-Cong Su, Guo Li, Saifullah, Bi-Feng Sun and Mu-Jiang-Shan Wang
Symmetry 2025, 17(8), 1344; https://doi.org/10.3390/sym17081344 - 17 Aug 2025
Viewed by 962
Abstract
Accurately predicting stock prices is crucial for investment and risk management, but the non-stationarity of the financial market and the complex correlations among stocks pose challenges to traditional models (ARIMA, LSTM, XGBoost), resulting in difficulties in effectively capturing dynamic patterns and limited prediction [...] Read more.
Accurately predicting stock prices is crucial for investment and risk management, but the non-stationarity of the financial market and the complex correlations among stocks pose challenges to traditional models (ARIMA, LSTM, XGBoost), resulting in difficulties in effectively capturing dynamic patterns and limited prediction accuracy. To this end, this paper proposes the Financial Spatio-Temporal Graph Attention Network (FSTGAT), with the following core innovations: temporal modelling through gated causal convolution to avoid future information leakage and capture long- and short-term fluctuations; enhanced spatial correlation learning by adopting the Dynamic Graph Attention Mechanism (GATv2) that incorporates industry information; designing the Multiple-Input-Multiple-Output (MIMO) architecture of industry grouping for the simultaneous learning of intra-group synergistic and inter-group influence; symmetrically fusing spatio-temporal modules to construct a hierarchical feature extraction framework. Experiments in the commercial banking and metals sectors of the New York Stock Exchange (NYSE) show that FSTGAT significantly outperforms the benchmark model, especially in high-volatility scenarios, where the prediction error is reduced by 45–69%, and can accurately capture price turning points. This study confirms the potential of graph neural networks to model the structure of financial interconnections, providing an effective tool for stock forecasting in non-stationary markets, and its forecasting accuracy and industry correlation capturing ability can support portfolio optimization, risk management improvement and supply chain decision guidance. Full article
(This article belongs to the Section Computer)
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21 pages, 2639 KB  
Article
A Hybrid Model of Multi-Head Attention Enhanced BiLSTM, ARIMA, and XGBoost for Stock Price Forecasting Based on Wavelet Denoising
by Qingliang Zhao, Hongding Li, Xiao Liu and Yiduo Wang
Mathematics 2025, 13(16), 2622; https://doi.org/10.3390/math13162622 - 15 Aug 2025
Viewed by 482
Abstract
The stock market plays a crucial role in the financial system, with its price movements reflecting macroeconomic trends. Due to the influence of multifaceted factors such as policy shifts and corporate performance, stock prices exhibit nonlinearity, high noise, and non-stationarity, making them difficult [...] Read more.
The stock market plays a crucial role in the financial system, with its price movements reflecting macroeconomic trends. Due to the influence of multifaceted factors such as policy shifts and corporate performance, stock prices exhibit nonlinearity, high noise, and non-stationarity, making them difficult to model accurately using a single approach. To enhance forecasting accuracy, this study proposes a hybrid forecasting framework that integrates wavelet denoising, multi-head attention-based BiLSTM, ARIMA, and XGBoost. Wavelet transform is first employed to enhance data quality. The multi-head attention BiLSTM captures nonlinear temporal dependencies, ARIMA models linear trends in residuals, and XGBoost improves the recognition of complex patterns. The final prediction is obtained by combining the outputs of all models through an inverse-error weighted ensemble strategy. Using the CSI 300 Index as an empirical case, we construct a multidimensional feature set including both market and technical indicators. Experimental results show that the proposed model clearly outperforms individual models in terms of RMSE, MAE, MAPE, and R2. Ablation studies confirm the importance of each module in performance enhancement. The model also performs well on individual stock data (e.g., Fuyao Glass), demonstrating promising generalization ability. This research provides an effective solution for improving stock price forecasting accuracy and offers valuable insights for investment decision-making and market regulation. Full article
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23 pages, 2216 KB  
Article
Development of Financial Indicator Set for Automotive Stock Performance Prediction Using Adaptive Neuro-Fuzzy Inference System
by Tamás Szabó, Sándor Gáspár and Szilárd Hegedűs
J. Risk Financial Manag. 2025, 18(8), 435; https://doi.org/10.3390/jrfm18080435 - 5 Aug 2025
Viewed by 550
Abstract
This study investigates the predictive performance of financial indicators in forecasting stock prices within the automotive sector using an adaptive neuro-fuzzy inference system (ANFIS). In light of the growing complexity of global financial markets and the increasing demand for automated, data-driven forecasting models, [...] Read more.
This study investigates the predictive performance of financial indicators in forecasting stock prices within the automotive sector using an adaptive neuro-fuzzy inference system (ANFIS). In light of the growing complexity of global financial markets and the increasing demand for automated, data-driven forecasting models, this research aims to identify those financial ratios that most accurately reflect price dynamics in this specific industry. The model incorporates four widely used financial indicators, return on assets (ROA), return on equity (ROE), earnings per share (EPS), and profit margin (PM), as inputs. The analysis is based on real financial and market data from automotive companies, and model performance was assessed using RMSE, nRMSE, and confidence intervals. The results indicate that the full model, including all four indicators, achieved the highest accuracy and prediction stability, while the exclusion of ROA or ROE significantly deteriorated model performance. These findings challenge the weak-form efficiency hypothesis and underscore the relevance of firm-level fundamentals in stock price formation. This study’s sector-specific approach highlights the importance of tailoring predictive models to industry characteristics, offering implications for both financial modeling and investment strategies. Future research directions include expanding the indicator set, increasing the sample size, and testing the model across additional industry domains. Full article
(This article belongs to the Section Economics and Finance)
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25 pages, 946 KB  
Article
Short-Term Forecasting of the JSE All-Share Index Using Gradient Boosting Machines
by Mueletshedzi Mukhaninga, Thakhani Ravele and Caston Sigauke
Economies 2025, 13(8), 219; https://doi.org/10.3390/economies13080219 - 28 Jul 2025
Viewed by 937
Abstract
This study applies Gradient Boosting Machines (GBMs) and principal component regression (PCR) to forecast the closing price of the Johannesburg Stock Exchange (JSE) All-Share Index (ALSI), using daily data from 2009 to 2024, sourced from the Wall Street Journal. The models are evaluated [...] Read more.
This study applies Gradient Boosting Machines (GBMs) and principal component regression (PCR) to forecast the closing price of the Johannesburg Stock Exchange (JSE) All-Share Index (ALSI), using daily data from 2009 to 2024, sourced from the Wall Street Journal. The models are evaluated under three training–testing split ratios to assess short-term forecasting performance. Forecast accuracy is assessed using standard error metrics: mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute scaled error (MASE). Across all test splits, the GBM consistently achieves lower forecast errors than PCR, demonstrating superior predictive accuracy. To validate the significance of this performance difference, the Diebold–Mariano (DM) test is applied, confirming that the forecast errors from the GBM are statistically significantly lower than those of PCR at conventional significance levels. These findings highlight the GBM’s strength in capturing nonlinear relationships and complex interactions in financial time series, particularly when using features such as the USD/ZAR exchange rate, oil, platinum, and gold prices, the S&P 500 index, and calendar-based variables like month and day. Future research should consider integrating additional macroeconomic indicators and exploring alternative or hybrid forecasting models to improve robustness and generalisability across different market conditions. Full article
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12 pages, 1066 KB  
Article
Prediction of the Maximum and Minimum Prices of Stocks in the Stock Market Using a Hybrid Model Based on Stacking
by Sebastian Tuesta, Nahum Flores and David Mauricio
Algorithms 2025, 18(8), 471; https://doi.org/10.3390/a18080471 - 28 Jul 2025
Viewed by 610
Abstract
Predicting stock prices on stock markets is challenging due to the nonlinear and nonstationary nature of financial markets. This study presents a hybrid model based on integrated machine learning (ML) techniques—neural networks, support vector regression (SVR), and decision trees—that uses the stacking method [...] Read more.
Predicting stock prices on stock markets is challenging due to the nonlinear and nonstationary nature of financial markets. This study presents a hybrid model based on integrated machine learning (ML) techniques—neural networks, support vector regression (SVR), and decision trees—that uses the stacking method to estimate the next day’s maximum and minimum stock prices. The model’s performance was evaluated using three data sets: Brazil’s São Paulo Stock Exchange (iBovespa)—Companhia Energética do Rio Grande do Norte (CSRN) and CPFL Energia (CPFE)—and one from the New York Stock Exchange (NYSE), the Dow Jones Industrial Average (DJI). The datasets covered the following time periods: CSRN and CPFE from 1 January 2008 to 30 September 2013, and DJI from 3 December 2018 to 31 August 2024. For the CSRN ensemble, the hybrid model achieved a mean absolute percentage error (MAPE) of 0.197% for maximum price and 0.224% for minimum price, outperforming results from the literature. For the CPFE set, the model showed a MAPE of 0.834% for the maximum price and 0.937% for the minimum price, demonstrating comparable accuracy. The model obtained a MAPE of 0.439% for the DJI set for maximum price and 0.474% for minimum price, evidencing its applicability across different market contexts. These results suggest that the proposed hybrid approach offers a robust alternative for stock price prediction by overcoming the limitations of using a single ML technique. Full article
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25 pages, 837 KB  
Article
DASF-Net: A Multimodal Framework for Stock Price Forecasting with Diffusion-Based Graph Learning and Optimized Sentiment Fusion
by Nhat-Hai Nguyen, Thi-Thu Nguyen and Quan T. Ngo
J. Risk Financial Manag. 2025, 18(8), 417; https://doi.org/10.3390/jrfm18080417 - 28 Jul 2025
Viewed by 1024
Abstract
Stock price forecasting remains a persistent challenge in time series analysis due to complex inter-stock relationships and dynamic textual signals such as financial news. While Graph Neural Networks (GNNs) can model relational structures, they often struggle with capturing higher-order dependencies and are sensitive [...] Read more.
Stock price forecasting remains a persistent challenge in time series analysis due to complex inter-stock relationships and dynamic textual signals such as financial news. While Graph Neural Networks (GNNs) can model relational structures, they often struggle with capturing higher-order dependencies and are sensitive to noise. Moreover, sentiment signals are typically aggregated using fixed time windows, which may introduce temporal bias. To address these issues, we propose DASF-Net (Diffusion-Aware Sentiment Fusion Network), a multimodal framework that integrates structural and textual information for robust prediction. DASF-Net leverages diffusion processes over two complementary financial graphs—one based on industry relationships, the other on fundamental indicators—to learn richer stock representations. Simultaneously, sentiment embeddings extracted from financial news using FinBERT are aggregated over an empirically optimized window to preserve temporal relevance. These modalities are fused via a multi-head attention mechanism and passed to a temporal forecasting module. DASF-Net integrates daily stock prices and news sentiment, using a 3-day sentiment aggregation window, to forecast stock prices over daily horizons (1–3 days). Experiments on 12 large-cap S&P 500 stocks over four years demonstrate that DASF-Net outperforms competitive baselines, achieving up to 91.6% relative reduction in Mean Squared Error (MSE). Results highlight the effectiveness of combining graph diffusion and sentiment-aware features for improved financial forecasting. Full article
(This article belongs to the Special Issue Machine Learning Applications in Finance, 2nd Edition)
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20 pages, 3775 KB  
Article
CIRGNN: Leveraging Cross-Chart Relationships with a Graph Neural Network for Stock Price Prediction
by Shanghui Jia, Han Gao, Jiaming Huang, Yingke Liu and Shangzhe Li
Mathematics 2025, 13(15), 2402; https://doi.org/10.3390/math13152402 - 25 Jul 2025
Viewed by 762
Abstract
Recent years have seen a rise in combining deep learning and technical analysis for stock price prediction. However, technical indicators are often prioritized over technical charts due to quantification challenges. While some studies use closing price charts for predicting stock trends, they overlook [...] Read more.
Recent years have seen a rise in combining deep learning and technical analysis for stock price prediction. However, technical indicators are often prioritized over technical charts due to quantification challenges. While some studies use closing price charts for predicting stock trends, they overlook charts from other indicators and their relationships, resulting in underutilized information for predicting stock. Therefore, we design a novel framework to address the underutilized information limitations within technical charts generated by different indicators. Specifically, different sequences of stock indicators are used to generate various technical charts, and an adaptive relationship graph learning layer is employed to learn the relationships among technical charts generated by different indicators. Finally, by applying a GNN model combined with the relationship graphs of diverse technical charts, temporal patterns of stock indicator sequences are captured, fully utilizing the information between various technical charts to achieve accurate stock price predictions. Additionally, we further tested our framework with real-world stock data, showing superior performance over advanced baselines in predicting stock prices, achieving the highest net value in trading simulations. Our research results not only complement the existing applications of non-singular technical charts in deep learning but also offer backing for investment applications in financial market decision-making. Full article
(This article belongs to the Special Issue Mathematical Modelling in Financial Economics)
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20 pages, 1840 KB  
Article
A Hybrid Long Short-Term Memory with a Sentiment Analysis System for Stock Market Forecasting
by Konstantinos Liagkouras and Konstantinos Metaxiotis
Electronics 2025, 14(14), 2753; https://doi.org/10.3390/electronics14142753 - 8 Jul 2025
Cited by 1 | Viewed by 843
Abstract
Addressing the stock market forecasting as a classification problem, where the model predicts the direction of stock price movement, is crucial for both traders and investors, as it can help them to allocate limited resources to the most promising investment opportunities. In this [...] Read more.
Addressing the stock market forecasting as a classification problem, where the model predicts the direction of stock price movement, is crucial for both traders and investors, as it can help them to allocate limited resources to the most promising investment opportunities. In this study, we propose a hybrid system that uses a Long Short-Term Memory (LSTM) network and sentiment analysis for predicting the direction of the movement of the stock price. The proposed hybrid system is fed with historical stock data and regulatory news announcements for producing more reliable responses. LSTM networks are well suited to handling time series data with long-term dependencies, while the sentiment analyser provides insights into how news impacts stock price movements by classifying business news into classes. By integrating both the LSTM network and the sentiment classifier, the proposed hybrid system delivers more accurate forecasts. Our experiments demonstrate that the proposed hybrid system outperforms other competing configurations. Full article
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16 pages, 808 KB  
Article
Enhancing Stock Price Forecasting with CNN-BiGRU-Attention: A Case Study on INDY
by Madilyn Louisa, Gumgum Darmawan and Bertho Tantular
Mathematics 2025, 13(13), 2148; https://doi.org/10.3390/math13132148 - 30 Jun 2025
Viewed by 687
Abstract
The stock price of PT Indika Energy Tbk (INDY) reflects the dynamics of Indonesia’s energy sector, which is heavily influenced by global coal price fluctuations, national energy policies, and geopolitical conditions. This study aimed to develop an accurate forecasting model to predict the [...] Read more.
The stock price of PT Indika Energy Tbk (INDY) reflects the dynamics of Indonesia’s energy sector, which is heavily influenced by global coal price fluctuations, national energy policies, and geopolitical conditions. This study aimed to develop an accurate forecasting model to predict the movement of INDY stock prices using a hybrid machine learning approach called CNN-BiGRU-AM. The objective was to generate future forecasts of INDY stock prices based on historical data from 28 August 2019 to 24 February 2025. The method applied a hybrid model combining a Convolutional Neural Network (CNN), Bidirectional Gated Recurrent Unit (BiGRU), and an Attention Mechanism (AM) to address the nonlinear, volatile, and noisy characteristics of stock data. The results showed that the CNN-BiGRU-AM model achieved high accuracy with a Mean Absolute Percentage Error (MAPE) below 3%, indicating its effectiveness in capturing long-term patterns. The CNN helped extract local features and reduce noise, the BiGRU captured bidirectional temporal dependencies, and the Attention Mechanism allocated weights to the most relevant historical information. The model remained robust even when stock prices were sensitive to external factors such as global commodity trends and geopolitical events. This study contributes to providing more accurate forecasting solutions for companies, investors, and stakeholders in making strategic decisions. It also enriches the academic literature on the application of deep learning techniques in financial data analysis and stock market forecasting within a complex and dynamic environment. Full article
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36 pages, 770 KB  
Review
Stock Market Prediction Using Machine Learning and Deep Learning Techniques: A Review
by Mohammadreza Saberironaghi, Jing Ren and Alireza Saberironaghi
AppliedMath 2025, 5(3), 76; https://doi.org/10.3390/appliedmath5030076 - 24 Jun 2025
Cited by 1 | Viewed by 11200
Abstract
The rapid advancement of machine learning and deep learning techniques has revolutionized stock market prediction, providing innovative methods to analyze financial trends and market behavior. This review paper presents a comprehensive analysis of various machine learning and deep learning approaches utilized in stock [...] Read more.
The rapid advancement of machine learning and deep learning techniques has revolutionized stock market prediction, providing innovative methods to analyze financial trends and market behavior. This review paper presents a comprehensive analysis of various machine learning and deep learning approaches utilized in stock market prediction, focusing on their methodologies, evaluation metrics, and datasets. Popular models such as LSTM, CNN, and SVM are examined, highlighting their strengths and limitations in predicting stock prices, volatility, and trends. Additionally, we address persistent challenges, including data quality and model interpretability, and explore emerging research directions to overcome these obstacles. This study aims to summarize the current state of research, provide insights into the effectiveness of predictive models. Full article
(This article belongs to the Special Issue Optimization and Machine Learning)
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44 pages, 3458 KB  
Article
Fractional Optimizers for LSTM Networks in Financial Time Series Forecasting
by Mustapha Ez-zaiym, Yassine Senhaji, Meriem Rachid, Karim El Moutaouakil and Vasile Palade
Mathematics 2025, 13(13), 2068; https://doi.org/10.3390/math13132068 - 22 Jun 2025
Viewed by 889
Abstract
This study investigates the theoretical foundations and practical advantages of fractional-order optimization in computational machine learning, with a particular focus on stock price forecasting using long short-term memory (LSTM) networks. We extend several widely used optimization algorithms—including Adam, RMSprop, SGD, Adadelta, FTRL, Adamax, [...] Read more.
This study investigates the theoretical foundations and practical advantages of fractional-order optimization in computational machine learning, with a particular focus on stock price forecasting using long short-term memory (LSTM) networks. We extend several widely used optimization algorithms—including Adam, RMSprop, SGD, Adadelta, FTRL, Adamax, and Adagrad—by incorporating fractional derivatives into their update rules. This novel approach leverages the memory-retentive properties of fractional calculus to improve convergence behavior and model efficiency. Our experimental analysis evaluates the performance of fractional-order optimizers on LSTM networks tasked with forecasting stock prices for major companies such as AAPL, MSFT, GOOGL, AMZN, META, NVDA, JPM, V, and UNH. Considering four metrics (Sharpe ratio, directional accuracy, cumulative return, and MSE), the results show that fractional orders can significantly enhance prediction accuracy for moderately volatile stocks, especially among lower-cap assets. However, for highly volatile stocks, performance tends to degrade with higher fractional orders, leading to erratic and inconsistent forecasts. In addition, fractional optimizers with short-memory truncation offer a favorable trade-off between computational efficiency and modeling accuracy in medium-frequency financial applications. Their enhanced capacity to capture long-range dependencies and robust performance in noisy environments further justify their adoption in such contexts. These results suggest that fractional-order optimization holds significant promise for improving financial forecasting models—provided that the fractional parameters are carefully tuned to balance memory effects with system stability. Full article
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