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45 pages, 17180 KB

Open AccessArticle

Regime-Dependent Graph Neural Networks for Enhanced Volatility Prediction in Financial Markets

by Pulikandala Nithish Kumar, Nneka Umeorah and Alex Alochukwu

Mathematics 2026, 14(2), 289; https://doi.org/10.3390/math14020289 - 13 Jan 2026

Viewed by 323

Accurate volatility forecasting is essential for risk management in increasingly interconnected financial markets. Traditional econometric models capture volatility clustering but struggle to model nonlinear cross-market spillovers. This study proposes a Temporal Graph Attention Network (TemporalGAT) for multi-horizon volatility forecasting, integrating LSTM-based temporal encoding [...] Read more.

Accurate volatility forecasting is essential for risk management in increasingly interconnected financial markets. Traditional econometric models capture volatility clustering but struggle to model nonlinear cross-market spillovers. This study proposes a Temporal Graph Attention Network (TemporalGAT) for multi-horizon volatility forecasting, integrating LSTM-based temporal encoding with graph convolutional and attention layers to jointly model volatility persistence and inter-market dependencies. Market linkages are constructed using the Diebold–Yilmaz volatility spillover index, providing an economically interpretable representation of directional shock transmission. Using daily data from major global equity indices, the model is evaluated against econometric, machine learning, and graph-based benchmarks across multiple forecast horizons. Performance is assessed using MSE,

R^{2}

, MAFE, and MAPE, with statistical significance validated via Diebold–Mariano tests and bootstrap confidence intervals. The study further conducts a strict expanding-window robustness test, comparing fixed and dynamically re-estimated spillover graphs in a fully out-of-sample setting. Sensitivity and scenario analyses confirm robustness across hyperparameter configurations and market regimes, while results show no systematic gains from dynamic graph updating over a fixed spillover network. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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26 pages, 2929 KB

Open AccessArticle

Label-Driven Optimization of Trading Models Across Indices and Stocks: Maximizing Percentage Profitability

by Abdulmohssen S. AlRashedy and Hassan I. Mathkour

Mathematics 2025, 13(23), 3889; https://doi.org/10.3390/math13233889 - 4 Dec 2025

Viewed by 1177

Abstract

Short-term trading presents a high-dimensional prediction problem, where the profitability of trading signals depends not only on model accuracy but also on how financial labels are defined and aligned with market dynamics. Traditional approaches often apply uniform modeling choices across assets, overlooking the [...] Read more.

Short-term trading presents a high-dimensional prediction problem, where the profitability of trading signals depends not only on model accuracy but also on how financial labels are defined and aligned with market dynamics. Traditional approaches often apply uniform modeling choices across assets, overlooking the asset-specific nature of volatility, liquidity, and market response. In this work, we introduce a structured, label-aware machine learning pipeline aimed at maximizing short-term trading profitability across four major benchmarks: S&P 500 (SPX), NASDAQ-100 (NDX), Dow Jones Industrial Average (DJI), and the Tadāwul All-Share Index (TASI and twelve of their most actively traded constituents). Our solution systematically evaluates all combinations of six model types (logistic regression, support vector machines, random forest, XGBoost, 1-D CNN, and LSTM), eight look-ahead labeling windows (3 to 10 days), and four feature subset sizes (44, 26, 17, 8 variables) derived through Random Forest permutation-importance ranking. Backtests are conducted using realistic long/flat simulations with zero commission, optimizing for Percentage Profit and Profit Factor on a 2005–2021 train/2022–2024 test split. The central contribution of the framework is a labeling-aware search mechanism that assigns to each asset its optimal combination of model type, look-ahead horizon, and feature subset based on out-of-sample profitability. Empirical results show that while XGBoost performs best on average, CNN and LSTM achieve standout gains on highly volatile tech stocks. The optimal look-ahead window varies by market from 3-day signals on liquid U.S. shares to 6–10-day signals on the less-liquid TASI universe. This joint model–label–feature optimization avoids one-size-fits-all assumptions and yields transferable configurations that cut grid-search cost when deploying from index level to constituent stocks, improving data efficiency, enhancing robustness, and supporting more adaptive portfolio construction in short-horizon trading strategies. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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32 pages, 8434 KB

Open AccessArticle

Explainable Machine Learning Financial Econometrics for Digital Inclusive Finance Impact on Rural Labor Market

by Huanhao Chen, Yong Chen, Jiaxuan Wu and Xiaofei Du

Mathematics 2025, 13(22), 3710; https://doi.org/10.3390/math13223710 - 19 Nov 2025

Viewed by 635

Abstract

The research examines how digital inclusive finance reshapes the rural labor market using an auditable index system and an interpretable learning pipeline. We construct a four-pillar framework for the rural labor market covering labor behavior, labor structure, security and fairness, and sustainability, and [...] Read more.

The research examines how digital inclusive finance reshapes the rural labor market using an auditable index system and an interpretable learning pipeline. We construct a four-pillar framework for the rural labor market covering labor behavior, labor structure, security and fairness, and sustainability, and compute county-level scores with an Attribute Hierarchy Model plus Fuzzy Comprehensive Evaluation (AHM–FCE). Using data for 58 counties in Jiangsu from 2014 to 2023, we estimate nonlinear links from overall and sub-dimensional digital finance to labor market outcomes with a random forest optimized by Particle Swarm Optimization plus Genetic Algorithm (PSO-GA-RF). Theoretical contribution: we provide a measurement-based bridge from digital inclusive finance to rural labor markets by aligning access, usage, and service quality with the four pillars of the rural labor market index, which yields testable county level predictions on participation, job quality, equity, and persistence of gains. Maps show heterogeneity, with higher behavior scores, lagging sustainability, and a north–south gradient. Empirically, stronger digital finance is associated with higher non-agricultural employment, better job quality, narrower urban–rural gaps, and stronger protection mechanisms, with larger effects where rural population shares and policy support are higher. Findings are robust to variable transforms, bandwidth choices, and tuning. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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22 pages, 1069 KB

Open AccessArticle

A Hybrid EGARCH–Informer Model with Consistent Risk Calibration for Volatility and CVaR Forecasting

by Ming Che Lee

Mathematics 2025, 13(19), 3108; https://doi.org/10.3390/math13193108 - 28 Sep 2025

Cited by 1 | Viewed by 1920

Abstract

This study proposes a hybrid EGARCH-Informer framework for forecasting volatility and calibrating tail risk in financial time series. The econometric layer (EGARCH) captures asymmetric and persistent volatility dynamics, while the attention layer (Informer) models long-range temporal dependence with sparse attention. The framework produces [...] Read more.

This study proposes a hybrid EGARCH-Informer framework for forecasting volatility and calibrating tail risk in financial time series. The econometric layer (EGARCH) captures asymmetric and persistent volatility dynamics, while the attention layer (Informer) models long-range temporal dependence with sparse attention. The framework produces horizon-specific forecasts (H = 1 and H = 5) that are mapped to VaR and CVaR at α = 0.95 and 0.99. Evaluation covers pointwise accuracy (MAE, RMSE) and risk coverage calibration (CVaR bias and Kupiec’s unconditional coverage), complemented by Conditional Coverage (CC) and Dynamic Quantile (DQ) diagnostics, and distributional robustness via a Student-t mapping of VaR/CVaR. Across four U.S. equity indices (SPX, IXIC, DJI, SOX), the hybrid matches GARCH at the short horizon and yields systematic error gains at the longer horizon while maintaining higher calibration quality than deep learning baselines. MAE and RMSE values remain near 0.0002 at H = 1, with relative improvements of 2–6% at H = 5. CVaR bias stays tightly bounded; DQ rarely rejects, and CC is stricter but consistent with clustered exceedances, and the Student-t results keep the median hit rates near nominal with small, mildly conservative CVaR biases. These findings confirm the hybrid model’s robustness and transferability across market conditions. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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23 pages, 3153 KB

Open AccessFeature PaperArticle

Robustness Study of Unit Elasticity of Intertemporal Substitution Assumption and Preference Misspecification

by Huarui Jing

Mathematics 2025, 13(10), 1593; https://doi.org/10.3390/math13101593 - 13 May 2025

Viewed by 882

Abstract

This paper proposes a novel robustness framework for studying the unit elasticity of intertemporal substitution (EIS) assumption based on the Perron-Frobenius sieve estimation model by Christensen, 2017. The sieve nonparametric decomposition is a central model that connects key strands of the long run [...] Read more.

This paper proposes a novel robustness framework for studying the unit elasticity of intertemporal substitution (EIS) assumption based on the Perron-Frobenius sieve estimation model by Christensen, 2017. The sieve nonparametric decomposition is a central model that connects key strands of the long run risk literature and recovers the stochastic discount factor (SDF) under the unit EIS assumption. I generate various economies based on Epstein–Zin preferences to simulate scenarios where the EIS deviates from unity. Then, I study the main estimation mechanism of the decomposition as well as the time discount factor and the risk aversion parameter estimation surface. The results demonstrate the robustness of estimating the average yield, change of measure, and preference parameters but also reveal an “absorption effect” arising from the unit EIS assumption. The findings highlight that asset pricing models assuming a unit EIS produce distorted parameter estimates, caution researchers about the potential under- or over-estimation of risk aversion, and provide insight into trends of misestimation when interpreting the results. I also identify an additional source of failure from a consumption component, which demonstrates a more general limit of the consumption-based capital asset pricing model and the structure used to estimate relevant preference parameters. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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26 pages, 1734 KB

Open AccessFeature PaperArticle

Explainable Domain Adaptation Learning Framework for Credit Scoring in Internet Finance Through Adversarial Transfer Learning and Ensemble Fusion Model

by Feiyang Xu and Runchi Zhang

Mathematics 2025, 13(7), 1045; https://doi.org/10.3390/math13071045 - 24 Mar 2025

Cited by 3 | Viewed by 2047

Abstract

Adversarial transfer learning is extensively applied in computer vision owing to its remarkable capability in addressing domain adaptation. However, its applications in credit scoring remain underexplored due to the complexity of financial data. The performance of traditional credit scoring models relies on the [...] Read more.

Adversarial transfer learning is extensively applied in computer vision owing to its remarkable capability in addressing domain adaptation. However, its applications in credit scoring remain underexplored due to the complexity of financial data. The performance of traditional credit scoring models relies on the consistency of domain distribution. Any shift in feature distribution leads to a degradation in model accuracy. To address this issue, we propose a domain adaptation framework comprising a transfer learner and a decision tree. The framework integrates the following: (1) feature partitioning through Wassertein relevance metric; (2) adversarial training of the transfer learner using features with significant distributional differences to achieve an inseparable representation of the source and target domains, while the remaining features are utilized for decision tree model training; and (3) a weighted voting method combines the predictions of the transfer learner and the decision tree. The Shapley Additive Explanations (SHAP) method was used to analyze the predictions of the model, providing the importance of individual features and insights into the model’s decision-making process. Experimental results show that our approach improves prediction accuracy by 3.5% compared to existing methods. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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14 pages, 982 KB

Open AccessArticle

Online Investor Sentiment via Machine Learning

by Zongwu Cai and Pixiong Chen

Mathematics 2024, 12(20), 3192; https://doi.org/10.3390/math12203192 - 12 Oct 2024

Cited by 1 | Viewed by 2396

Abstract

In this paper, we propose utilizing machine learning methods to determine the expected aggregated stock market risk premium based on online investor sentiment and employing the multifold forward-validation method to select the relevant hyperparameters. Our empirical studies provide strong evidence that some machine [...] Read more.

In this paper, we propose utilizing machine learning methods to determine the expected aggregated stock market risk premium based on online investor sentiment and employing the multifold forward-validation method to select the relevant hyperparameters. Our empirical studies provide strong evidence that some machine learning methods, such as extreme gradient boosting or random forest, show significant predictive ability in terms of their out-of-sample performances with high-dimensional investor sentiment proxies. They also outperform the traditional linear models, which shows a possible unobserved nonlinear relationship between online investor sentiment and risk premium. Moreover, this predictability based on online investor sentiment has a better economic value, so it improves portfolio performance for investors who need to decide the optimal asset allocation in terms of the certainty equivalent return gain and the Sharpe ratio. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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27 pages, 4774 KB

Open AccessArticle

A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

by Tao Chen, Yixuan Li and Renfang Tian

Mathematics 2023, 11(20), 4386; https://doi.org/10.3390/math11204386 - 22 Oct 2023

Viewed by 2192

Abstract

Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we [...] Read more.

Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we propose a simple solution based on functional data analysis (FDA) and truncated Taylor series expansions. It is demonstrated through a simulation study that our proposed method is superior—compared with misspecified parametric methods—in fitting and forecasting continuous-time stochastic processes, while the parametric method slightly dominates under correct specification, with comparable forecast errors to the FDA-based method. Due to its generally consistent and more robust performance against possible misspecification, the proposed FDA-based method is recommended in the presence of modeling discrepancy. Further, we apply the proposed method to predict the future return of the S&P 500, utilizing observations extracted from a latent continuous-time process, and show the practical efficacy of our approach in accurately discerning the underlying dynamics. Full article

(This article belongs to the Special Issue Financial Econometrics and Machine Learning)

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