Search Results (97)

This paper introduces a new unit-Burr distortion function constructed via a transformation of the Burr random variable. The distortion can be applied to existing base copulas to create new copula families. The relationships of tail dependence coefficients and tail orders between the base bivariate copula and the unit-Burr distorted copula are derived. The unit-Burr distortion-induced family of copulas includes well-known copula classes, such as the BB1, BB2, and BB4 copulas, as special cases. The unit-Burr distortion of existing bivariate copulas may result in a family of copulas with both lower and upper tail coefficients ranging from 0 to 1. An empirical application to the rates of return for Microsoft and Google stocks is presented. Full article

Estimating heterogeneous treatment effects (HTEs) across multiple correlated outcomes poses significant challenges due to complex dependency structures and diverse data types. In this study, we propose a novel deep learning framework integrating empirical copula transformations with a CNN-LSTM (Convolutional Neural Networks and Long Short-Term Memory networks) architecture to capture nonlinear dependencies and temporal dynamics in multivariate treatment effect estimation. The empirical copula transformation, a rank-based nonparametric approach, preprocesses input covariates to better represent the underlying joint distributions before modeling. We compare this method with a baseline CNN-LSTM model lacking copula preprocessing and a nonparametric tree-based approach, the Causal Forest, grounded in generalized random forests for HTE estimation. Our framework accommodates continuous, count, and censored survival outcomes simultaneously through a multitask learning setup with customized loss functions, including Cox partial likelihood for survival data. We evaluate model performance under varying treatment perturbation rates via extensive simulation studies, demonstrating that the Empirical Copula CNN-LSTM achieves superior accuracy and robustness in average treatment effect (ATE) and conditional average treatment effect (CATE) estimation. These results highlight the potential of copula-based deep learning models for causal inference in complex multivariate settings, offering valuable insights for personalized treatment strategies. Full article

Settlement analyses of foundation soils are very important for the investigation, design, and construction of buildings. However, due to complex natural sedimentary processes, soil-forming environments, and geological tectonic stress histories, settlement properties show obvious spatial variability and autocorrelation. Moreover, measurement data on the physical and mechanical parameters of building foundation soils are limited. This limits the accuracy of formation stability analyses and safety evaluations. In this study, a series of field tests of building foundation soils were carried out, and the statistical physical and mechanical properties of the clay strata were obtained. A random field method and copula functions of uncertain geotechnical properties with limited survey data are proposed. A dual-yield surface constitutive model of the soil properties and a stability analysis method for uncertain deformation were developed. The detailed analytical procedures for soil deformation and stratum settlement are presented. The reliability functions and failure probabilities of variable settlement processes are calculated and analyzed. The impact of the spatial variation and cross-correlation of geotechnical properties on the probabilistic stability of variable land subsidence is discussed. This work presents an innovative analysis approach for evaluating the variable settlement properties of building foundation soils. The results show that the four different mechanical parameters can be regressed to linear equations. The horizontal fluctuation scale is significantly larger than the vertical scale. Copula theory provides a powerful framework for modeling limited geotechnical parameters. The bootstrap approach avoids parametric assumptions, leveraging empirical data to enhance the reliability analysis of variable settlement. The variability parameter exerts a greater influence on land subsidence processes than the correlation structure. The failure probabilities of variable stratum settlement for different cross-correlations of building foundation soils are different. These results provide an important reference for the safety of building engineering. Full article

Online learning has become increasingly prevalent in real-world applications, where data streams often comprise heterogeneous feature types—both nominal and numerical—and labels may not arrive synchronously with features. However, most existing online learning methods assume homogeneous data types and synchronous arrival of features and labels. In practice, data streams are typically heterogeneous and exhibit asynchronous label feedback, making these methods insufficient. To address these challenges, we propose a novel algorithm, termed Online Asynchronous Learning over Streaming Nominal Data (OALN), which maps heterogeneous data into a continuous latent space and leverages a model pool alongside a hint mechanism to effectively manage asynchronous labels. Specifically, OALN is grounded in three core principles: (1) It utilizes a Gaussian mixture copula in the latent space to preserve class structure and numerical relationships, thereby addressing the encoding and relational learning challenges posed by mixed feature types. (2) It performs adaptive imputation through conditional covariance matrices to seamlessly handle random missing values and feature drift, while incrementally updating copula parameters to accommodate dynamic changes in the feature space. (3) It incorporates a model pool and hint mechanism to efficiently process asynchronous label feedback. We evaluate OALN on twelve real-world datasets; the average cumulative error rates are 23.31% and 28.28% under the missing rates of 10% and 50%, respectively, and the average AUC scores are 0.7895 and 0.7433, which are the best results among the compared algorithms. And both theoretical analyses and extensive empirical studies confirm the effectiveness of the proposed method. Full article

We propose a novel contextual multi-armed bandit (CMAB) framework that integrates copula-based context generation with Gaussian Process (GP) regression for reward modeling, addressing complex dependency structures and uncertainty in sequential decision-making. Context vectors are generated using Gaussian and vine copulas to capture nonlinear dependencies, while arm-specific reward functions are modeled via GP regression with Beta-distributed targets. We evaluate three widely used bandit policies—Thompson Sampling (TS), $\epsilon$-Greedy, and Upper Confidence Bound (UCB)—on simulated environments informed by real-world datasets, including Boston Housing and Wine Quality. The Boston Housing dataset exemplifies heterogeneous decision boundaries relevant to housing-related marketing, while the Wine Quality dataset introduces sensory feature-based arm differentiation. Our empirical results indicate that the $\epsilon$-Greedy policy consistently achieves the highest cumulative reward and lowest regret across multiple runs, outperforming both GP-based TS and UCB in high-dimensional, copula-structured contexts. These findings suggest that combining copula theory with GP modeling provides a robust and flexible foundation for data-driven sequential experimentation in domains characterized by complex contextual dependencies. Full article

In this article, an R-vine copula model is proposed to detect the nonlinear interrelationships between the oil market and five Chinese new-energy-related stock markets from 2017 to 2022, i.e., photovoltaic, new energy vehicles, energy storage, wind power, and nuclear power industries. Firstly, the transmission of downward and upward risk spillover effects (RSEs) is measured from the oil market to the five Chinese new-energy-related stock markets. Subsequently, a CoVaR backtesting methodology is developed to demonstrate the availability of the R-vine copula-CoVaR model. The empirical studies strongly show that the oil market exhibits a significant asymmetric RSE on the five Chinese new-energy-related stock markets. Furthermore, different Chinese new-energy-related stock markets have varying responses to the positive and negative impacts of the oil market. Specifically, the photovoltaic, energy storage, and wind power industries are more sensitive to such adverse effects. However, the new energy vehicle and nuclear power industries are more likely to be positively affected. Full article

Scatter plots are widely recognized as fundamental tools for illustrating the relationship between two numerical variables. Despite this, based on solid theoretical foundations, scatter plots generated from pairs of continuous random variables may not serve as reliable tools for assessing dependence. Sklar’s theorem implies that scatter plots created from ranked data are preferable for such analysis, as they exclusively convey information pertinent to dependence. This is in stark contrast to conventional scatter plots, which also encapsulate information about the variables’ marginal distributions. Such additional information is extraneous to dependence analysis and can obscure the visual interpretation of the variables’ relationship. In this article, we delve into the theoretical underpinnings of these ranked data scatter plots, hereafter referred to as rank plots. We offer insights into interpreting the information they reveal and examine their connections with various association measures, including Pearson’s and Spearman’s correlation coefficients, as well as Schweizer–Wolff’s measure of dependence. Furthermore, we introduce a novel visualization ensemble, termed a d-plot, which integrates rank plots, empirical copula diagnostics, and traditional summaries to provide a comprehensive visual assessment of dependence between continuous variables. This ensemble facilitates the detection of subtle dependence structures, including non-quadrant dependencies, that might be overlooked by traditional visual tools. Full article

With the growing global emphasis on sustainable development goals, Environmental, Social, and Governance (ESG) factors have emerged as critical considerations in shaping economic policies and strategies. This study employs the ARMA-eGARCH-skewed t and Vine Copula models, combined with the CoVaR method, to investigate the dependence structure and risk spillover pathways across various industrial sectors in China within the ESG framework. By modeling the complex interdependencies among sectors, this research uncovers the relationships between individual industries and the ESG benchmark index, while also analyzing the correlations across different sectors. Furthermore, this study quantifies the risk contagion effects across distinct industries under extreme market conditions and maps the pathways of risk spillovers. The findings highlight the pivotal role of ESG considerations in shaping industrial structures. Empirical results demonstrate that industries such as agriculture, energy, and manufacturing exhibit significant systemic risk characteristics in response to ESG fluctuations. Specifically, the identified risk spillover pathway follows the sequence: agriculture → consumption → ESG → manufacturing → energy. The CoVaR values for agriculture, energy, and manufacturing indicate a significant potential for risk contagion. Moreover, sectors such as real estate, finance, and information technology exhibit significant risk spillover effects. These findings offer valuable empirical evidence and a theoretical foundation for formulating ESG-related policies. This study suggests that effective risk management, promoting green finance, encouraging technological innovation, and optimizing industrial structures can significantly mitigate systemic risks. These measures can contribute to maintaining industrial stability and fostering sustainable economic development. Full article

The accurate and stable prediction of crude oil prices holds significant value, providing insightful guidance for investors and decision-makers. The intricate interplay of factors influencing oil prices and the pronounced fluctuations present significant obstacles within the realm of oil price forecasting. This study introduces a novel hybrid model framework, distinct from the conventional methods, that integrates influencing factors for oil price prediction. First, using Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) extract mode components from crude oil prices. Second, using the Adaptive Copula-based Feature Selection (ACBFS), rooted in Copula theory, facilitates the integration of the influencing factors; ACBFS enhances both accuracy and stability in feature selection, thereby amplifying predictive performance and interpretability. Third, low-frequency modes are predicted through an Attention Mechanism-based Long and Short-Term Memory Neural Network (AM-LSTM), optimized using Bayesian Optimization and Hyperband (BOHB). Conversely, high-frequency modes are forecasted using Extreme Gradient Boosting Models (XGboost). Finally, the error correction mechanism further enhances the predictive accuracy. The experimental results show that the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) of the proposed hybrid prediction framework are the lowest compared to the benchmark model, at 0.7333 and 1.1069, respectively, which proves that the designed prediction structure has better efficiency and higher accuracy and stability. Full article

Supply chain finance (SCF) operations require extensive activities and a high level of information transparency, making them vulnerable to operational issues that pose significant risks of financial loss for commercial banks. Accurately assessing operational risks is crucial for ensuring market stability. This research aims to provide a reliable operational risk assessment tool for commercial banks’ SCF businesses and to deeply examine the features of operational risk events. To achieve these goals, the study explores the dependency structure of risk cells and proposes a quantitative measurement framework for operational risk in SCF. The loss distribution analysis (LDA) is improved to align with the marginal loss distribution of segmented operational risks at both high and low frequencies. A tailored copula function is developed to capture the dependency structure between various risk cells, and the Monte Carlo algorithm is utilized to compute operational risk values. An empirical investigation is conducted using SCF loss data from commercial banks, creating a comprehensive database documenting over 400 entries of SCF loss events from 2012 to 2022. This database is analyzed to identify behaviors, trends, frequencies, and the severity of loss events. The results indicate that fraud risk and compliance risk are the primary sources of operational risks in SCF. The proposed approach is validated through backtesting, revealing a value at risk of CNY 179.3 million and an expected shortfall of CNY 204.9 million at the 99.9% significance level. This study pioneers the measurement of SCF operational risk, offering a comprehensive view of operational risks in SCF and providing an effective risk management tool for financial institutions and policymakers. Full article

This study introduces a novel approach to estimate tail dependence in financial contagion using mixture copulas. Addressing the challenges of weight parameter estimation in conventional models, we propose a Bayesian model averaging method to determine optimal copula weights. Through both simulations and empirical studies, the proposed method demonstrates improved robustness and accuracy, particularly when handling extreme weight scenarios. These advancements offer more reliable measurements of financial contagion, contributing to enhanced risk management and policy-making in interconnected financial markets. Full article

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO₂ emissions in addition to examining these series for entropy, long-range dependence, fractionality, complexity, chaos, and nonlinearity with a dataset spanning from 25 June 2012 to 22 June 2024. Empirical results from Shannon, Rényi, and Tsallis entropy measures; Kolmogorov–Sinai complexity; Hurst–Mandelbrot and Lo’s R/S tests; and Phillips’ and Geweke and Porter-Hudak’s fractionality tests confirm the presence of entropy, complexity, fractionality, and long-range dependence. Further, the largest Lyapunov exponents and Hurst exponents confirm chaos across all series. The BDS test confirms nonlinearity, and ARCH-type heteroskedasticity test results support the basis for the use of novel TAR-TR-GARCH–copula causality. The model estimation results indicate moderate to strong levels of positive and asymmetric tail dependence and contagion under distinct regimes. The novel method captures nonlinear causality dynamics from Bitcoin and Fintech to energy consumption and CO₂ emissions as well as causality from energy consumption to CO₂ emissions and bidirectional feedback between Bitcoin and Fintech. These findings underscore the need to take the chaotic and complex dynamics seriously in policy and decision formulation and the necessity of eco-friendly technologies for Bitcoin and Fintech. Full article

Liaoning Province, a crucial agricultural region in Northeast China, has endured frequent drought disasters in recent years, significantly affecting both agricultural production and the ecological environment. Conducting drought research is of paramount importance for formulating scientific drought monitoring and prevention strategies, ensuring agricultural production and ecological safety. This study developed a Comprehensive Joint Drought Index (CJDI) using the empirical Copula function to systematically analyze drought events in Liaoning Province from 1981 to 2020. Through the application of MK trend tests, Morlet wavelet analysis, and run theory, the spatiotemporal variation patterns and recurrence characteristics of drought in Liaoning Province were thoroughly investigated. The results show that, compared to the three classic drought indices, Standardized Precipitation Index (SPI), Evaporative Demand Drought Index (EDDI), and Standardized Precipitation Evapotranspiration Index (SPEI), CJDI has the highest accuracy in monitoring actual drought events. From 1981 to 2020, drought intensity in all regions of Liaoning Province (east, west, south, and north) exhibited an upward trend, with the western region experiencing the most significant increase, as evidenced by an MK test Z-value of −4.53. Drought events in Liaoning Province show clear seasonality, with the most significant periodic fluctuations in spring (main cycles of 5–20 years, longer cycles of 40–57 years), while the frequency and variability of drought events in autumn and winter are lower. Mild droughts frequently occur in Liaoning Province, with joint and co-occurrence recurrence periods ranging from 1.0 to 1.8 years. Moderate droughts have shorter joint recurrence periods in the eastern region (1.2–1.4 years) and longer in the western and southern regions (1.4–2.2 years), with the longest co-occurrence recurrence period in the southern region (3.0–4.0 years). Severe and extreme droughts are less frequent in Liaoning Province. This study provides a scientific foundation for drought monitoring and prevention in Liaoning Province and serves as a valuable reference for developing agricultural production strategies to adapt to climate change. Full article

The composition of high rockfill dam materials is complex, and the mechanical parameters are uncertain and correlated in unknown ways due to the influences of the environment and construction, leading to complex deformation mechanisms in the dam–foundation system. Statistical characteristics of material parameters are the basis for deformation and stress analysis of high core rockfill dams, and using an inaccurate distribution model may result in erroneous analysis results. Furthermore, empirically evaluated distribution types of parameters are susceptible to the influence of small sample sizes, which are common in the statistics of geotechnical engineering. Therefore, proposing a multi-dimensional joint distribution model for parameters based on small-sample data is of great importance. This study determined the interval estimation values of Duncan–Chang E-B model parameters—such as the mean value and coefficient of variation for the core wall, rockfill, and overburden materials—using parameter statistical analysis, bootstrap sampling methods, and Akaike information criterion (AIC) optimization. Additionally, the marginal distribution types of each parameter were identified. Subsequently, a multi-dimensional joint distribution model for Duncan–Chang model parameters was constructed based on the multi-dimensional nonlinear correlation analysis of parameters and the Copula function theory. The application results for the PB dam demonstrate that joint sampling can effectively reflect the inherent correlation laws of material parameters, and that the results for stress and deformation are reasonable, leading to a sound evaluation of the cracking risk in the core wall of high core rockfill dams. Full article

Financial markets are increasingly interlinked. Therefore, this study explores the complex relationships between the Tadawul All Share Index (TASI), West Texas Intermediate (WTI) crude oil prices, and Bitcoin (BTC) returns, which are pivotal to informed investment and risk-management decisions. Using copula-based models, this study identified Student’s t copula as the most appropriate one for encapsulating the dependencies between TASI and BTC and between TASI and WTI prices, highlighting significant tail dependencies. For the BTC–WTI relationship, the Frank copula was found to have the best fit, indicating nonlinear correlation without tail dependence. The predictive power of the identified copulas were compared to that of Long Short-Term Memory (LSTM) networks. The LSTM models demonstrated markedly lower Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Scaled Error (MASE) across all assets, indicating higher predictive accuracy. The empirical findings of this research provide valuable insights for financial market participants and contribute to the literature on asset relationship modeling. By revealing the most effective copulas for different asset pairs and establishing the robust forecasting capabilities of LSTM networks, this paper sets the stage for future investigations of the predictive modeling of financial time-series data. The study highlights the potential of integrating machine-learning techniques with traditional econometric models to improve investment strategies and risk-management practices. Full article