Search Results (145)

Volatility modelling is a key feature of financial risk management, portfolio optimisation, and forecasting, particularly for market indices such as the JSE Top40 Index, which serves as a benchmark for the South African stock market. This study investigates volatility modelling of the JSE Top40 Index log-returns from 2011 to 2025 using a hybrid approach that integrates statistical and machine learning techniques through a two-step approach. The ARMA(3,2) model was chosen as the optimal mean model, using the auto.arima() function from the forecast package in R (version 4.4.0). Several alternative variants of GARCH models, including sGARCH(1,1), GJR-GARCH(1,1), and EGARCH(1,1), were fitted under various conditional error distributions (i.e., STD, SSTD, GED, SGED, and GHD). The choice of the model was based on AIC, BIC, HQIC, and LL evaluation criteria, and ARMA(3,2)-EGARCH(1,1) was the best model according to the lowest evaluation criteria. Residual diagnostic results indicated that the model adequately captured autocorrelation, conditional heteroskedasticity, and asymmetry in JSE Top40 log-returns. Volatility persistence was also detected, confirming the persistence attributes of financial volatility. Thereafter, the ARMA(3,2)-EGARCH(1,1) model was coupled with XGBoost using standardised residuals extracted from ARMA(3,2)-EGARCH(1,1) as lagged features. The data was split into training (60%), testing (20%), and calibration (20%) sets. Based on the lowest values of forecast accuracy measures (i.e., MASE, RMSE, MAE, MAPE, and sMAPE), along with prediction intervals and their evaluation metrics (i.e., PICP, PINAW, PICAW, and PINAD), the hybrid model captured residual nonlinearities left by the standalone ARMA(3,2)-EGARCH(1,1) and demonstrated improved forecasting accuracy. The hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost model outperforms the standalone ARMA(3,2)-EGARCH(1,1) model across all forecast accuracy measures. This highlights the robustness and suitability of the hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost model for financial risk management in emerging markets and signifies the strengths of integrating statistical and machine learning methods in financial time series modelling. Full article

This research evaluates the suitability of Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) for improving financial return predictions across 15 major worldwide stock indices. The proposed method uses graph modeling to represent financial index relationships which enables the detection of symmetric market dependencies including mutual spillover effects and bidirectional influence patterns. The symmetric network structures become most important during financial instability because market interdependencies strengthen at such times. The evaluation process compares these models against XGBoost and Multi-Layer Perceptron (MLP) and Support Vector Machine (SVM) traditional forecasting approaches. The results of 30 time-series cross-validation experiments show that GNN models produce lower RMSE and MAE values, especially during financial crises and recovery phases and volatile market periods. The models show reduced advantages when markets remain stable. The research demonstrates that graph-based forecasting models which incorporate symmetry effectively detect complex financial relationships which leads to important implications for investment strategies and financial risk management and global economic forecasting. Full article

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 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

This study proposes a novel hybrid forecasting approach designed explicitly for long-horizon financial time series. It incorporates LMD (Local Mean Decomposition), SD (Signal Decomposition), and sophisticated machine learning methods. The framework for the NASDAQ Composite Index begins by decomposing the original time series into stochastic and deterministic components using the LMD approach. This method effectively separates linear and nonlinear signal structures. The stochastic components are modeled using ARIMA to represent linear temporal dynamics, while the deterministic components are projected using cutting-edge machine learning methods, including XGBoost, Random Forest (RF), Artificial Neural Networks (ANNs), and Support Vector Machines (SVMs). This study employs various statistical metrics to evaluate the predictive ability across both short-term noise and long-term trends, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Directional Statistic (DS). Furthermore, the Diebold–Mariano test is used to determine the statistical significance of any forecast improvements. Empirical results demonstrate that the hybrid LMD–ARIMA–SD–XGBoost model consistently outperforms alternative configurations in terms of prediction accuracy and directional consistency. These findings demonstrate the advantages of integrating decomposition-based signal filtering with ensemble machine learning to improve the robustness and generalizability of long-term forecasting. This study presents a scalable and adaptive approach for modeling complex, nonlinear, and high-dimensional time series, thereby contributing to the enhancement of intelligent forecasting systems in the economic and financial sectors. As far as the authors are aware, this is the first study to combine XGBoost and LMD in a hybrid decomposition framework for forecasting long-horizon stock indexes. Full article

This study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influence on financial markets remains contested. This research adopts a multi-method analytical framework combining algebraic combinatorics and time-series econometrics. The methodology incorporates the construction of a directed credit rating transition graph, the partially ordered set representation of rating hierarchies, rolling-window correlation analysis, Granger causality testing, event study evaluation, and the formulation of a reward matrix with optimal rating path optimization. Empirical results indicate that credit rating announcements in Greece exert only modest short-term effects on the Athens Stock Exchange General Index, implying that markets often anticipate these changes. In contrast, sequential downgrade trajectories elicit more pronounced and persistent market responses. The reward matrix and path optimization approach reveal structured investor behavior that is sensitive to the cumulative pattern of rating changes. These findings offer a more nuanced interpretation of how sovereign credit risk is processed and priced in transparent and fiscally disciplined environments. By bridging network-based algebraic structures and economic data science, the study contributes a novel methodology for understanding systemic financial signals within sovereign credit systems. Full article

Forecasting financial time series is challenging due to their intrinsic nonlinearity, high volatility, and complex dependencies across temporal scales. This study introduces MSGformer, a novel hybrid architecture that integrates multi-scale graph neural networks (MSGNet) with Transformer encoders to capture both local temporal fluctuations and long-term global trends in high-frequency financial data. The MSGNet module constructs multi-scale representations using adaptive graph convolutions and intra-sequence attention, while the Transformer component enhances long-range dependency modeling via multi-head self-attention. We evaluate MSGformer on minute-level stock index data from the Chinese A-share market, including CSI 300, SSE 50, CSI 500, and SSE Composite indices. Extensive experiments demonstrate that MSGformer significantly outperforms state-of-the-art baselines (e.g., Transformer, PatchTST, Autoformer) in terms of MAE, RMSE, MAPE, and R². The results confirm that the proposed hybrid model achieves superior prediction accuracy, robustness, and generalization across various forecasting horizons, providing an effective solution for real-world financial decision-making and risk assessment. Full article

Existing stock volatility forecasting models predominantly rely on same-frequency market data while neglecting mixed-frequency integration and face particular challenges in incorporating low-frequency macroeconomic variables that exhibit temporal mismatches with financial market dynamics. To address this limitation, this study develops a novel hybrid approach for stock market volatility forecasting, which synergistically combines a deep learning model (CNN-BiLSTM-Attention) with the GARCH-MIDAS model. The GARCH-MIDAS model can fully exploit mixed-frequency information, including daily returns, monthly macroeconomic variables, and EPU. The deep learning model can effectively capture both spatial and temporal patterns of multivariate time-series data, thus effectively improving prediction accuracy and generalization ability in stock market volatility forecasting. The results indicate that the CNN-BiLSTM-Attention model yields the most accurate forecasts compared to the benchmark models. Furthermore, incorporating additional predictors, such as macroeconomic indicators and the Economic Policy Uncertainty Index, also provides valuable information for stock market volatility prediction, notably enhancing the model’s forecasting effect. Full article

Stock market forecasting has always been researched extensively in Social Sciences. In this research, Fuzzy time series with deep learning is widely adopted to create a fuzzy convolutional neural network integration model as this model enhances the fuzzification of values to enhance feature characteristics using two-dimensional input data in convolutional neural networks (CNNs). This allows the model to retain complete feature information. The fuzzy convolutional neural network (FCNN) model autonomously learns and extracts crucial features by integrating stock market data, resulting in improved forecasting accuracy. In this study, the model was tested for forecasting the Taiwan Weighted Stock Index and metrics such as the mean squared error (MSE) and mean absolute error (MAE), and the results were compared with the real data. The results showed that the model provided accurate predictions. Full article

In this paper, we propose a novel fuzzy time series forecasting model that integrates fuzzy C-means (FCM) clustering, the principle of justifiable granularity (PJG), and particle swarm optimization (PSO), with a focus on leveraging symmetry in subinterval partitioning to enhance model interpretability and forecasting accuracy. First, the FCM method is employed to partition the universe of discourse, generating an initial division of subintervals. To ensure symmetric information representation, triangular fuzzy information granules are constructed for these subintervals in accordance with the principle of justifiable granularity. Then, an objective function is formulated for the entire universe of discourse, and the PSO algorithm is utilized to optimize the subinterval division, resulting in the final optimal partition. This process ensures that the subintervals achieve a balance between coverage and specificity, thereby introducing a form of symmetry in the partitioning of the universe of discourse. Leveraging the optimized symmetric partition, the framework of the fuzzy time series model is implemented for forecasting. Finally, the proposed approach is carried out on the Taiwan Weighted Stock Index (TAIEX) datasets and the Shanghai Composite Index (SHCI) datasets. The forecasting results demonstrate that the proposed approach achieves higher prediction accuracy and semantic accuracy compared with other methods. Full article

Accurate stock price prediction requires the integration of heterogeneous data streams, yet conventional techniques struggle to simultaneously leverage fine-grained micro-stock features and broader macroeconomic indicators. To address this gap, we propose MambaLLM, a novel framework that fuses macro-index and micro-stock inputs through the synergistic use of state-space models (SSMs) and large language models (LLMs). Our two-branch architecture comprises (i) Micro-Stock Encoder, a Mamba-based temporal encoder for processing granular stock-level data (prices, volumes, and technical indicators), and (ii) Macro-Index Analyzer, an LLM module—employing DeepSeek R1 7B distillation—capable of interpreting market-level index trends (e.g., S&P 500) to produce textual summaries. These summaries are then distilled into compact embeddings via FinBERT. By merging these multi-scale representations through a concatenation mechanism and subsequently refining them with multi-layer perceptrons (MLPs), MambaLLM dynamically captures both asset-specific price behavior and systemic market fluctuations. Extensive experiments on six major U.S. stocks (AAPL, AMZN, MSFT, TSLA, GOOGL, and META) reveal that MambaLLM delivers up to a 28.50% reduction in RMSE compared with suboptimal models, surpassing traditional recurrent neural networks and MAMBA-based baselines under volatile market conditions. This marked performance gain highlights the framework’s unique ability to merge structured financial time series with semantically rich macroeconomic narratives. Altogether, our findings underscore the scalability and adaptability of MambaLLM, offering a powerful, next-generation tool for financial forecasting and risk management. Full article

Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time series’s next value by analysing its past. The input financial data are assumed to be consistent with an $\alpha$-stable Lévy motion. The computation of the scaling exponent and the value of $\alpha$, which characterises the type of the $\alpha$-stable Lévy motion, are crucial for the iterative scheme. These two indices can be determined at each iteration from the form of the structure function, for the computation of which we use the method of generalised moments. Their values are used for the creation of the corresponding $\alpha$-stable Lévy noise, which acts as a seed for the stochastic component. Furthermore, the drift and diffusion terms are calculated at each iteration. The proposed model is general, allowing the kind of stochastic process to vary from one iterative step to another, and its applicability is not restricted to financial data. As a case study, we consider Greece’s stock market general index over a period of five years, from September 2019 to September 2024, after the completion of bailout programmes. Greece’s economy changed from a restricted to a free market over the chosen era, and its stock market trading increments are likely to be describable by an $\alpha$-stable L’evy motion. We find that $\alpha =2$ and the scaling exponent H varies over time for every iterative step we perform. The forecasting points follow the same trend, are in good agreement with the actual data, and for most of the forecasts, the percentage error is less than 2%. Full article

This study examines the impact of the coronavirus disease 2019 (COVID-19) pandemic on market efficiency by analyzing three time series—price returns, absolute returns, and volatility increments—in the stock (Deutscher Aktienindex, Nikkei 225, Shanghai Stock Exchange (SSE), and Volatility Index) and cryptocurrency (Bitcoin and Ethereum) markets. The effect is found to vary by asset class and market. In the stock market, while the pandemic did not influence the Hurst exponent of volatility increments, it affected that of returns and absolute returns (except in the SSE, where returns remained unaffected). In the cryptocurrency market, the pandemic did not alter the Hurst exponent for any time series but influenced the strength of multifractality in returns and absolute returns. Some Hurst exponent time series exhibited a gradual decline over time, complicating the assessment of pandemic-related effects. Consequently, segmented analyses by pandemic period may erroneously suggest an impact, warranting caution in period-based studies. Full article

With the advancement of deep learning, its application in financial market forecasting has become a research hotspot. This paper proposes an innovative Multi-Scale TsMixer model for predicting stock index futures in the A-share market, covering SSE50, CSI300, and CSI500. By integrating Multi-Scale time-series features across the short, medium, and long term, the model effectively captures market fluctuations and trends. Moreover, since stock index futures reflect the collective movement of their constituent stocks, we introduce a novel approach: predicting individual constituent stocks and merging their forecasts using three fusion strategies (average fusion, weighted fusion, and weighted decay fusion). Experimental results demonstrate that the weighted decay fusion method significantly improves the prediction accuracy and stability, validating the effectiveness of Multi-Scale TsMixer. Full article

This study investigates the properties of financial markets that arise from the multi-scale structure of volatility, particularly intermittency, by employing robust theoretical tools from nonequilibrium thermodynamics. Intermittency in velocity fields along spatial and temporal axes is a well-known phenomenon in developed turbulence, with extensive research dedicated to its structures and underlying mechanisms. In turbulence, such intermittency is explained through energy cascades, where energy injected at macroscopic scales is transferred to microscopic scales. Similarly, analogous cascade processes have been proposed to explain the intermittency observed in financial time series. In this work, we model volatility cascade processes in the stock market by applying the framework of stochastic thermodynamics to a Langevin system that describes the dynamics. We introduce thermodynamic concepts such as temperature, heat, work, and entropy into the analysis of financial markets. This framework allows for a detailed investigation of individual trajectories of volatility cascades across longer to shorter time scales. Further, we conduct an empirical study primarily using the normalized average of intraday logarithmic stock prices of the constituent stocks in the FTSE 100 Index listed on the London Stock Exchange (LSE), along with two additional data sets from the Tokyo Stock Exchange (TSE). Our Langevin-based model successfully reproduces the empirical distribution of volatility—defined as the absolute value of the wavelet coefficients across time scales—and the cascade trajectories satisfy the Integral Fluctuation Theorem associated with entropy production. A detailed analysis of the cascade trajectories reveals that, for the LSE data set, volatility cascades from larger to smaller time scales occur in a causal manner along the temporal axis, consistent with known stylized facts of financial time series. In contrast, for the two data sets from the TSE, while similar behavior is observed at smaller time scales, anti-causal behavior emerges at longer time scales. Full article