ABSTRACT Global climate change has intensified the frequency and severity of compound dry‐hot events (CDHEs), posing more severe impacts on terrestrial ecosystems than individual extremes, particularly in Northwest China (NWC). However, a comprehensive probabilistic assessment of vegetation vulnerability under CDHEs, particularly, the identification of triggering thresholds for vegetation loss remains limited. This study employed standardised indices of vegetation (NDVI), drought (SPI) and hot conditions (STI) from 1982 to 2018 to develop a Vine copula framework for assessing vegetation vulnerability under CDHEs and identifying the corresponding triggering thresholds for vegetation loss. The results demonstrated that the standardised compound event indicator (SCEI) in NWC indicated a decreasing trend (−0.12 decade −1 ), reflecting the intensification of CDHEs. This intensification of CDHEs has led to greater ecosystem vulnerability in NWC. Under Severe Dry‐Severe Hot conditions (S4: SPI < −1.3 and STI > 1.3), the average probabilities of vegetation loss below the 50th, 30th, 20th and 10th percentiles were 51.2%, 42.3%, 36.2% and 27.2%, respectively. Different vegetation types (croplands, forests and grasslands) exhibited distinct vulnerability patterns, with grasslands being the most sensitive and forests the least. The average SPI/STI thresholds corresponding to vegetation loss below the 50th percentile (mild) and 10th percentile (extreme) were −0.71/0.72 and −1.08/1.35, respectively. It could provide a novel framework for assessing vegetation vulnerability under CDHEs, while simultaneously offering a profound comprehension of ecosystems' response mechanisms to CDHEs.

Carbon emission prediction based on spatial–temporal pattern recognition and novel integrated vine copula

This study introduces a novel forecasting framework, a Vine Copula (VC)-based Multivariate Deep Learning (MDL) model optimized using a Genetic Algorithm (GA), referred to as the Optimal GA-MDL-VC model. The model leverages GA to fine-tune the hyperparameters of various MDL architectures, including Multivariate Long Short-Term Memory (MLSTM), Multivariate Gated Recurrent Unit (MGRU), and Multivariate Recurrent Neural Network (MRNN). The integration of Vine Copulas with these GA-MDL variants enables the model to effectively capture complex interdependencies among multiple time series, thereby enhancing forecasting accuracy. An empirical study using daily modal price data of soybean – a globally significant agricultural commodity – across 15 major Indian markets demonstrates the superior forecasting accuracy of the proposed Optimal GA-MDL-VC model. Performance was evaluated against GA-MDL and traditional Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) models using two data splits: 80:10:10 and 70:15:15 for training, validation, and testing. The Optimal GA-MDL-VC model consistently outperformed the other models.

Resilience assessment of highway roads affected by slope failures induced by mainshock-aftershock sequences: insights from vine copula fragility surfaces

Multi-objective planning and optimal configuration of wind, solar, and energy storage in interconnected microgrid clusters using Vine Copula scenario generation and antlion optimization

The high penetration rate of renewable energy poses significant challenges to the planning and operation of power systems in regions with scarce data. In these regions, it is impossible to accurately simulate the complex nonlinear dependencies among hydro–wind–solar energy resources, which leads to huge operational risks and investment uncertainties. To bridge this gap, this study proposes a new data-driven framework that embeds the natural climate cycle (24 solar terms) into a physically consistent scenario generation process, surpassing the traditional linear approach. This framework introduces the Comprehensive Similarity Distance (CSD) indicator to quantify the curve similarity of power amplitude, pattern trend, and fluctuation position, thereby improving the K-means clustering. Compared with the K-means algorithm based on the standard Euclidean distance, the accuracy of the improved clustering pattern extraction is increased by 3.8%. By embedding the natural climate cycle and employing a two-stage dimensionality reduction architecture: time compression via improved clustering and feature fusion via Kernel PCA, the framework effectively captures cross-source dependencies and preserves climatic periodicity. Finally, combined with the simplified Vine Copula model, high-fidelity joint scenarios with a normalized root mean square error (NRMSE) of less than 3% can be generated. This study provides a reliable and computationally feasible tool for stochastic optimization and reliability analysis in the planning and operation of future power systems with high renewable energy grid integration.

Retraction Note: Unraveling the Interplay of Knowledge and Innovation in the Global Financial System: A Vine Copula Analysis of Sino-US Financial Risk Contagion

Single-cell RNA sequencing (scRNA-seq) has become an indispensable tool for studying biological systems at the cellular level. It has therefore has become increasingly important to develop accurate statistical models of scRNA-seq data. While many models have been proposed to characterize transcript expression of individual genes, comparatively little attention has been paid to modeling gene coexpression. Copula modeling offers a flexible approach to modeling gene coexpression by linking models of individual genes together using copula functions. Despite the growing popularity of copula models, their utility for modeling scRNA-seq data has not been thoroughly explored. Here we evaluated six copula models on their ability to model gene coexpression in scRNA-seq data. Using a diverse collection of reference datasets, we evaluated each copula model’s accuracy and efficiency in reproducing gene coexpression patterns. Our results show that Gaussian copulas provide the best balance between accuracy and speed, with more flexible but expensive copula models providing only a marginal improvement in accuracy while requiring a much longer time to fit. Vine copulas show promise in being able to achieve high accuracy, but current implementations are unable to scale to the large size of typical scRNA-seq datasets.

This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally intensive procedures limiting their practical use, we address this challenge through parallel computing techniques. To demonstrate our approach, we employ thirteen bivariate copula families within an R-vine pair-copula construction, applied to a large number of marginal distributions. The margins are modeled as exponential-type GARCH processes with intertemporal capital asset pricing specifications, using a mixture of Gaussian and generalized Pareto distributions. Results from an empirical study involving 100 financial returns confirm the effectiveness of our approach.

Probabilistic evaluation of agricultural drought using meteorological drought propagation mechanisms and Vine Copula in a compound drought framework

This research develops a vine copula regression framework for predicting intra-day volatility using multivariate high-frequency time series. The model incorporates lagged covariates and eigenfunctions obtained from multivariate functional principal component analysis (MFPCA). The MFPCA eigenfunctions capture hidden dependence structures and explain major variations in multivariate functional data, while vine copula regression provides a flexible, non-linear, and distribution-free tool for modeling highly correlated and non-normal covariates. To demonstrate the effectiveness of the proposed method, we analyze intra-day volatilities of the Korea Composite Stock Price Index based on 1-min log-return data, with covariates from Samsung Electronics, SK Hynix, and Hyundai Motor. In addition, we introduce a vine copula regression residual control chart that integrates MFPCA eigenfunctions and lagged covariates, enabling the detection of outliers and structural changes in functional time series. The real data application highlights the practical utility of the proposed approach for volatility forecasting and monitoring.

Economic Policy Uncertainty (EPU) captures the unpredictability of government decisions that shape market expectations and investment dynamics. In the energy sector, elevated policy uncertainty amplifies volatility, especially in oil markets where regulatory and geopolitical changes directly influence production, pricing, and trade. Meanwhile, renewable energy markets, represented by indices such as ICLN, respond asymmetrically to policy signals, depending heavily on the consistency of climate commitments and fiscal incentives. This study investigates the multiscale and nonlinear linkages among U.S. EPU, oil market volatility (OVX), and clean energy performance (ICLN). Using a hybrid GARCH–Wavelet–Vine Copula framework with the Maximal Overlap Discrete Wavelet Transform (MODWT), we examine horizon-dependent dependencies across short-, medium-, and long-term frequencies. The proposed model captures both the temporal persistence of volatility and cross-market co-movements driven by policy shocks. Empirical results suggest that surges in U.S. EPU significantly increase oil market volatility and indirectly weaken clean energy stability. Policy reversals, such as the U.S. withdrawal from the Paris Agreement, are found to heighten uncertainty spillovers between oil and renewable markets. The findings highlight that persistent policy uncertainty not only affects investor confidence and portfolio allocation but may also slow the ecological transition by discouraging long-term energy investments.

Increasing climate change leads to the variability of dependencies among meteorological factors. Currently, the investigation of the interdependence of meteorological variables primarily focuses on the bivariate relationships, such as precipitation and temperature or precipitation and wind speed. However, the high-dimensional dependencies among multiple meteorological factors have not been thoroughly explored. This paper proposes a statistical analysis framework that comprehensively analyzes the changes in dependencies among meteorological factors. This statistical analysis framework is based on multivariate joint distributions and enables the detection of dependency change points as well as the analysis of drivers using total probability formulations and orthogonal experiments. Taking the Huang-Huai-Hai region, a recipient area of the South-to-North Water Diversion project, as the study area, we constructed a vine copula-based multivariate joint distribution for precipitation (Pre) and six meteorological factors: temperature (Tm), maximum temperature (Tmax), minimum temperature (Tmin), wind speed (Win), relative humidity (Rhu), and the Southern Oscillation Index (SOI). The results indicate that a change point exists in the dependence of the 7-dimensional variables (Pre and six meteorological factors) in the Huang-Huai-Hai region in 2013. Tmin, Win, and Tmax are the primary driving factors affecting the precipitation–meteorological dependency relationship. The cumulative distribution function (CDF) is used to describe the probability distribution of precipitation and related meteorological factors. The optimal CDF values of the multivariate joint distribution model were achieved with Rhu and Tmax at level 3, SOI and Tm at level 2, and Win and Tmin at level 1. The results can provide a theoretical method for testing the non-stationarity of high-dimensional meteorological variable dependencies and offer conditional probability support for constructing meteorological prediction machine learning models.

A stochastic weather generator provides data by capturing statistical properties of observed weather patterns, enabling the simulation of realistic time series beyond the historic record. Such simulated weather data can be valuable in many fields (e.g., agriculture and energy), where multiple variables (e.g., temperature and precipitation) influence the production processes. Here, we present a new European simulated dataset for temperature, precipitation and wind speed, generated by the MYRIAD-Stochastic vIne-copula Model (MYRIAD-SIM). MYRIAD-SIM captures both spatiotemporal and multivariate dependencies with the use of conditional vine copulas, a statistical tool. The statistical properties of the MYRIAD-SIM data closely resembles ERA5-Land data while maintaining sufficient variability to explore possible alternative scenarios. The simulated data can facilitate new insights in, for example, compound climate event research, by providing multivariate weather events across different conditions.

Predicting road crash severity remains a major challenge in transportation safety research, requiring models that combine predictive accuracy, interpretability, and computational efficiency. This study introduces a Multi-Risk Index based on Copula Integration (MRI-Copula)—a hybrid framework that integrates Categorical Boosting (CatBoost) with SHapley Additive exPlanations (SHAP) and Vine Copula dependence modeling to assess and predict crash severity. The approach leverages CatBoost–SHAP to quantify the marginal contribution of each risk factor while maintaining model transparency and employs copula-based tail dependence to capture the joint escalation of risk under extreme crash conditions. Using a dataset of 877 police-reported crashes from Jeddah, Saudi Arabia, the framework constructs three interpretable sub-indices—Environmental Risk Index (ERI), Behavioural Risk Index (BRI), and Systemic Risk Index (SRI)—representing distinct domains of crash causation. These indices are combined through a convex weighting parameter (α), optimized via cross-validation (optimal α = 0.80), ensuring a balanced integration of predictive and dependence-based information. Comparative evaluation across multiple classifiers—CatBoost, Light Gradient Boosting Machine (LightGBM), Histogram-based Gradient Boosting (HistGB), and Logistic Regression—demonstrated the robustness of the framework. The CatBoost + MRI-Copula configuration achieved the highest predictive performance (AUC = 0.986; F1 = 0.904), while LightGBM and HistGB offered comparable accuracy (AUC ≈ 0.958; F1 ≈ 0.89) at a fraction of the computational time (≤1 s versus 32 s for CatBoost), highlighting a trade-off between analytical precision and scalability. Consequently, the MRI-Copula framework provides a transparent and theoretically grounded foundation for data-driven road safety management. It bridges predictive analytics and decision support offering a scalable, interpretable, and policy-relevant tool for proactive crash risk mitigation.

Stochastic simulation framework for renewable power output: Integrating hybrid discrete-continuous distributions with vine copula function

ABSTRACT The conventional Cox proportional hazards model is designed to measure the influence of factors on the timing of an event and focuses more on relative risk rather than absolute risk. In the presence of multiple time-to-event variables, this study introduces a copula-based extension of the standard Cox model, which facilitates the dependence structure between variables. We employ vine copulas to effectively model the potentially non-linear relationships between failure times. Through conducting simulation studies, we show that our new algorithm greatly improves the accuracy of predicting failure times compared to other existing methodologies. Our findings are applied to predict mortality timing in real medical data.

Evaluating Systemic Risk with Conditional Value at Risk and Vine Copulas in the Iranian Banking Network

ABSTRACT This paper investigates the risk spillover effects among nine biofuel-related assets across three countries. Both dependence structure and tail causal relations are studied with the stationary vine (S-vine) copula model and the quantile Granger causality test. The modified conditional value-at-risk (CoVaR) is proposed to measure the intertemporal risk spillover effects. It extends the traditional CoVaR to account for intertemporal dynamics. Comparatively, the traditional CoVaR may overestimate the risk spillover effects. The empirical results exhibit geographical clusters and potential paths of risk spillovers among biofuel-related assets. The spillover path runs from American markets to Chinese markets via the Malaysian market. American soybean oil is the risk transmitter, while Chinese palm oil is the primary risk recipient. Moreover, the spillover effects of downside risks have increased since the COVID-19. This research provides significant implications for risk management and investment in the biofuel-related markets.

Contextual multi-armed bandits (CMABs) are vital for sequential decision-making in areas such as recommendation systems, clinical trials, and finance. We propose a simulation framework integrating Gaussian Process (GP)-based CMABs with vine copulas to model dependent contexts and GARCH processes to capture reward volatility. Rewards are generated via copula-transformed Beta distributions to reflect complex joint dependencies and skewness. We evaluate four policies—ensemble, Epsilon-greedy, Thompson, and Upper Confidence Bound (UCB)—over 10,000 replications, assessing cumulative regret, observed reward, and cumulative reward. While Thompson sampling and LLM-guided policies consistently minimize regret and maximize rewards under varied reward distributions, Epsilon-greedy shows instability, and UCB exhibits moderate performance. Enhancing the ensemble with copula features, GP models, and dynamic policy selection driven by a large language model (LLM) yields superior adaptability and performance. Our results highlight the effectiveness of combining structured probabilistic models with LLM-based guidance for robust, adaptive decision-making in skewed, high-variance environments.