D-vine Copula Research Articles

Evaluating time-to-event surrogates for time-to-event true endpoints: an information-theoretic approach based on causal inference.

Putative surrogate endpoints must undergo a rigorous statistical evaluation before they can be used in clinical trials. Numerous frameworks have been introduced for this purpose. In this study, we extend the scope of the information-theoretic causal-inference approach to encompass scenarios where both outcomes are time-to-event endpoints, using the flexibility provided by D-vine copulas. We evaluate the quality of the putative surrogate using the individual causal association (ICA)-a measure based on the mutual information between the individual causal treatment effects. However, in spite of its appealing mathematical properties, the ICA may be ill defined for composite endpoints. Therefore, we also propose an alternative rank-based metric for assessing the ICA. Due to the fundamental problem of causal inference, the joint distribution of all potential outcomes is only partially identifiable and, consequently, the ICA cannot be estimated without strong unverifiable assumptions. This is addressed by a formal sensitivity analysis that is summarized by the so-called intervals of ignorance and uncertainty. The frequentist properties of these intervals are discussed in detail. Finally, the proposed methods are illustrated with an analysis of pooled data from two advanced colorectal cancer trials. The newly developed techniques have been implemented in the R package Surrogate.

Vine copula based structural equation models

Gaussian linear structural equation models (SEMs) are often used as a statistical model associated with a directed acyclic graph (DAG) also known as a Bayesian network. However, such a model might not be able to represent the non-Gaussian dependence present in some data sets resulting in nonlinear, non-additive and non Gaussian conditional distributions. Therefore the use of the class of D-vine copula based regression models for the specification of the conditional distribution of a node given its parents is proposed. This class extends the class of standard linear regression models considerably. The approach also allows to create an importance order of the parents of each node and gives the potential to remove edges from the starting DAG not supported by the data. Further uncertainty of conditional estimates can be assessed and fast generative simulation using the D-vine copula based SEM is available. The improvement over a Gaussian linear SEM is shown using random specifications of the D-vine based SEM as well as its ability to correctly remove edges not present in the data generation using simulation. An engineering application showcases the usefulness of the proposals.

Joint meta-analysis of two diagnostic tests accounting for within and between studies dependence.

There is an extensive literature on methods for meta-analysis of diagnostic test accuracy, but it mainly focuses on a single test. A multinomial generalised linear mixed model was recently proposed for the joint meta-analysis of studies comparing two tests on the same participants in a paired tests design with a gold standard. In this setting, we propose a novel model for joint meta-analysis of studies comparing two diagnostic tests which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the latent vector of probabilities of each combination of test results in diseased and non-diseased patients. For the random effects distribution of the latent proportions, we employ a one-truncated D-vine copula that can provide tail dependence or asymmetry. The proposed model includes the multinomial generalised linear mixed model as a special case, accounts for the within-study dependence induced because the tests are applied to the same participants, allows for between-studies dependence, and can also operate on the original scale of the latent proportions. The latter enables the derivation of summary receiver operating characteristic curves. Our methodology is demonstrated with simulation studies and a meta-analysis of screening for Down's syndrome with two tests: shortened humerus and shortened femur.

A framework for drought monitoring and assessment from a drought propagation perspective under non-stationary environments

According to the coupled influence of climate variation and anthropogenic activities, hydro-meteorological variables are hard to keep stationary in a changing environment. Consequently, the efficacy of traditional standardized drought indices, predicated upon the assumption of stationarity, has been called into question. In China, the challenge of drought monitoring and declaration is exacerbated by the need for multiple drought indices covering meteorological, agricultural, hydrological, and groundwater aspects, often lacking real-time availability. To address these challenges, we developed a framework for drought monitoring and assessment from a drought propagation perspective. Central to this is the Nonstationary Integrated Drought Index (NIDI), which integrates responses from meteorological, agricultural, hydrological, and groundwater droughts, accounting for climate change and anthropogenic influences. First, we analyse the process of drought propagation to select the suitable time scale standardized drought index. Subsequently, significant large-scale climatic indices are selected through linear and nonlinear correlation analyses to identify climate anomalies. Anthropogenic influences are assessed using indicators such as the Normalized Difference Vegetation Index (NDVI), Impervious Surface Ratio (ISR), and population density (POP). Nonstationary probability models are then developed for precipitation, soil moisture, runoff, and groundwater series, incorporating climatic and human-induced factors. Finally, the NIDI is calculated using a D-vine copula model, with parameter estimation and updating facilitated by a genetic algorithm, representing the temporal dependence structure among the variables. A case study in the Hulu River Basin of western China validated the NIDI. Results showed that the NIDI effectively accounts for nonstationary hydro-meteorological variables due to climate change and human activities, accurately reproducing their time-dependent structure. Compared to conventional indices like SPI, SSI, SRI, and SGI, the NIDI identifies more extreme drought events. In conclusion, the presented NIDI offers a more comprehensive approach to drought identification, providing valuable insights for accurate drought detection and effective drought-related policy-making.

Hedging crude oil and currencies fluctuations

Relying on the D-Vine copula model, this paper delves into the hedging capabilities of Brent crude oil against the exchange rate of oil-exporting and oil-importing nations. The results affirm Brent crude oil’s role as a safeguard and a refuge against the fluctuations of major currencies. Furthermore, we reaffirm that oil retains its robust hedging and safe-haven attributes during times of crisis, with currency co-movements across all countries exhibiting greater correlation than during the entire dataset. Additionally, our empirical findings highlight an unusually positive correlation between Brent crude oil and the Russian exchange rate during the Russia-Ukraine conflict, demonstrating that oil functions as a less effective hedge and a less dependable refuge for the Russian exchange rate in such geopolitical turbulence.

Wind speed monitoring using entropy theory and a copula-based approach

In this study, wind speeds in the Lut desert (Iran) was monitored at the Bam, Tabas and Birjand stations during the period 1973–2020 using entropy theory. The conventional entropy method was improved by considering the interaction between stations by a copula-based approach. Two different methods were examined for this purpose: 1) A trivariate vine copula was used to evaluate the interaction among the stations. For this purpose, a d-vine copula was considered to simulate the wind speed at each station as a function of the wind speed at the other stations. 2) A bivariate copula was used to model the simulated and observed wind speed at each station. In particular, a Frank copula was used to perform the joint probability analysis. The results indicate that implementing the proposed method for wind speed monitoring increases the Information Transfer Index (ITI) by approximately 24 %, 10 %, and 33 % at the Bam, Birjand, and Tabas stations, respectively, compared to using the conventional entropy method.

Multivariate degradation system reliability analysis with multiple sources of uncertainty

As the industrial Internet of Things evolves, multi-sensor monitoring becomes increasingly prevalent, resulting in degrading systems frequently exhibiting multivariate degradation characteristics. Multiple performance characteristics are frequently interdependent due to the consistency of the operating environment, operating conditions, and internal structure of the system. On the other hand, performance characteristic detection is also affected by numerous uncertainties. A multivariate stochastic degradation model that takes dependencies with multiple sources of uncertainty into account is developed for the analysis of multivariately dependent degradation systems. To represent linear or nonlinear degradation qualities, the marginal degradation process is referred to as a generalized stochastic degradation model. By using the D-vine copula function and pair-copula construction, dependencies between numerous variables are formed. The marginal and joint distribution parameters of the degradation model are derived using a two-step parameter estimation procedure. Lastly, the C-MAPSS dataset is used to analyze the applicability of the proposed model for bivariate and multivariate instances. The effectiveness of the proposed method is verified by experiments.

A comprehensive comparison of copula models and multivariate normal distribution for geo-material parametric data

Multivariate distribution models for geo-material parametric data play a crucial role in reliability-based design. Currently, two major models are commonly used: the conventional multivariate normal distribution model and the copula model (including subtypes like the elliptical copula model and Vine copula model). This study aims to assess the performance of different models including three specific copula models (Gaussian copula, t copula, and D-Vine copula models) and the conventional normal distribution model. To this end, this study employs an incomplete database comprising 693 data samples related to lacustrine soils near Dianchi Lake in Kunming city, China. Results indicate that copula models generally exhibit lower model uncertainty compared to the conventional multivariate normal distribution model. Using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), the elliptical copula ranks first, followed by Gaussian copula, with D-Vine copula ranking third. For a balanced evaluation of performance and complexity, the conventional multivariate normal distribution model is favored. This study provides valuable insights for selecting appropriate models for geo-material parametric data, aiding reliability-based design in geotechnical engineering. Additionally, it is demonstrated that sampling with replacement in the Bootstrapping technique has only a slight effect on the estimation of correlation matrices for the incomplete database.

Developing an earthquake model based on simultaneous peak ground acceleration occurrences using the D-vine copula approach

Developing an earthquake model based on simultaneous peak ground acceleration occurrences using the D-vine copula approach

Diversification in financial and crypto markets

This article investigates the conditional value at risk (CVaR) of two portfolio optimiza- tion approaches containing assets from the financial and crypto markets. We first catch the conditional interdependence structure among each variable through the vine-copula-GARCH model before merging it with the Mean-CVaR model. We then optimize each portfolio and find out the optimal allocation while evaluating the precise risk. The results indicate that the D-Vine copula is more suitable for both portfolios and that, when different conditional stock indices information are being taken into consideration, the crypto-market components can act as a weak hedge/safe haven against financial market indices. Furthermore, as CVaR is found to outperform the mean-variance of Markowitz in both portfolios, both risk measures similarly show that when including cryptocurrencies in a portfolio, the S&P 500 shall not be included. Additionally, the inclusion of Ethereum in a portfolio already containing Bitcoin does not boost the return.

Imputation of missing values in environmental time series by D-vine copulas

Missing values in environmental time series are common and must be imputed before carrying out an analysis requiring complete data. We propose an imputation method for the time series of a target station using information of neighboring stations measuring the same variable. The method allows these neighboring stations to have missing values themselves. The multivariate dataset comprising the time series of the target station and its neighboring stations is jointly modeled by a vine copula and parametric margins. Multiple imputation takes into account the uncertainty of missing data by generating several plausible values for each missing value in the time series of the target station. This is done in a Bayesian framework by sampling the posterior distribution of a missing value, which is conditional on the observed stations for the date. The method is suitable for extremes because the vine copula can model the eventual tail dependence between stations. The application to a skew surge time series is presented, with cross-validated results and a focus on the performance for the upper extremes.

The Stability of Islamic Cryptocurrencies and Copula-Based Dependence with Alternative Crypto and Fiat Currencies

Purpose — This study aims to examine Islamic cryptocurrencies and their dependency on foreign exchange markets in vine copula architecture (CD-Vine) and provide a framework for detecting complex dependence structures, risk management implications, and hedging effectiveness. Design/Methodology/Approach — This study used gold-backed cryptocurrencies and three fiat currencies. The vine copula approach was preferred because it applies several distributions and estimates complex dependencies. Hedging effectiveness was measured by constructing simulation-based portfolios optimised with DCC-t-Copula. Benford’s law and realized variance were used to determine the stability of Islamic cryptocurrencies. Findings — According to C-Vine and D-Vine copula models, paper money has a weak tail dependence with gold-backed cryptocurrencies. Only OneGram coin, whose volatility matched the risk of Bitcoin, showed zero irregularities in volume trading. The findings were robust to different estimations based on Minimum Spanning Tree and Dendrogram. Originality/Value — This is the first study to examine Islamic cryptocurrencies’ stability and the significance of hedging effectiveness on gold-backed cryptocurrencies under a copula-based approach. Research Limitations — The study did not apply time-varying vine copula. Practical Implications — The risk management perspective shows insignificant hedge effectiveness in the portfolio of fiat and gold-backed cryptocurrencies.

Application of vine copulas to estimate dew point temperature

In this study, the accuracy of the copula-based model in the simulation of the dew point temperature in various climates of Iran was investigated, using simulations based on vine copulas such as C-, D-, and R-vine copulas. By examining the various vine copulas and their tree sequences, the best copula and best tree sequence based on AIC, BIC, and log-likelihood were selected. The results show that based on the complete similarity in our case between C-, D- and R-vine copulas, the selected best C-vine copulas fit well the dependence between the minimum and maximum air temperatures and dew point temperature. The simulation results were analyzed using root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE) coefficient, and violin plots. The results show that the copula-based model has high accuracy at all stations. The min (max) RMSE is related to Kerman (Ahvaz) station with RMSE = 0.396 oC (0.617 oC). Also, the min (max) NSE is related to Ahvaz (Urmia) station with NSE = 0.925 (0.955). Also, according to the violin plot, it is possible to appreciate the acceptable certainty of the copula-based model. Due to the diversity of the tree sequences of vine copulas and the use of the rotated states of the internal vine copulas, as well as the possibility of interfering with the effective parameters in high dimensions, the simulation results are reliable and have no restrictions. This model can be used as the best model to estimate dew point temperature due to the full coverage of the range of changes in data.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow. However, existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months. To address this limitation, this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations. This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas. The up-to-down sequential method, which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach, was used to determine the structures of multivariate D-vine copulas. The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station, the inflow control station of the Longyangxia Reservoir in the Yellow River Basin. The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow. This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Downside Risk and Portfolio Optimization of Energy Stocks: A Study on the Extreme Value Theory and the Vine Copula Approach

ABSTRACT Energy stocks are potentially a hedge against inflation and have a number of advantages over other forms of energy investing. This motivates us to study on portfolio management of energy stocks. We compare the performance of proposed GARCH-EVT-vine copula models under three different dimensions with other competing models using energy stocks from the U.S. market. In our proposed model, we use static C- and D-vine copulas. We compare the accuracy and efficiency of different models in forecasting portfolio VaR and CVaR. We also examine whether the proposed models yield greater economic and statistical performances than the competing models in a tactical asset allocation framework. Our findings indicate that the proposed models perform best overall. In fact, the relatively better performance of the proposed model is even more prominent when the portfolio size increases. Further, the comparative analysis between GARCHEVT-static vine and GARCH-EVT-dynamic vine copula models produces mixed results.

A multivariate frequency-severity framework for healthcare data breaches

Data breaches in healthcare have become a substantial concern in recent years and cause millions of dollars in financial losses each year. It is fundamental for government regulators, insurance companies, and stakeholders to understand the breach frequency and the number of affected individuals in each state, as these are directly related to the federal Health Insurance Portability and Accountability Act (HIPAA) and state data breach laws. However, an obstacle to studying data breaches in healthcare is the lack of suitable statistical approaches. We develop a novel multivariate frequency-severity framework to analyze breach frequency and the number of affected individuals at the state level. A mixed effects model is developed to model the square root transformed frequency, and the log-gamma distribution is proposed to capture the skewness and heavy tail exhibited by the distribution of numbers of affected individuals. We further discover a positive nonlinear dependence between the transformed frequency and the log-transformed numbers of affected individuals (i.e., severity). In particular, we propose to use a D-vine copula to capture the multivariate dependence among conditional severities, given frequencies due to its inherent temporal structure and rich bivariate copula families. The rejection sampling technique is developed to simulate the predictive distributions. Both the in-sample and out-of-sample studies show that the proposed multivariate frequency-severity model that accommodates nonlinear dependence has satisfactory fitting and prediction performances.

Trivariate Joint Distribution Modelling of Compound Events Using the Nonparametric D-Vine Copula Developed Based on a Bernstein and Beta Kernel Copula Density Framework

Low-lying coastal communities are often threatened by compound flooding (CF), which can be determined through the joint occurrence of storm surges, rainfall and river discharge, either successively or in close succession. The trivariate distribution can demonstrate the risk of the compound phenomenon more realistically, rather than considering each contributing factor independently or in pairwise dependency relations. Recently, the vine copula has been recognized as a highly flexible approach to constructing a higher-dimensional joint density framework. In these, the parametric class copula with parametric univariate marginals is often involved. Its incorporation can lead to a lack of flexibility due to parametric functions that have prior distribution assumptions about their univariate marginal and/or copula joint density. This study introduces the vine copula approach in a nonparametric setting by introducing Bernstein and Beta kernel copula density in establishing trivariate flood dependence. The proposed model was applied to 46 years of flood characteristics collected on the west coast of Canada. The univariate flood marginal distribution was modelled using nonparametric kernel density estimation (KDE). The 2D Bernstein estimator and beta kernel copula estimator were tested independently in capturing pairwise dependencies to establish D-vine structure in a stage-wise nesting approach in three alternative ways, each by permutating the location of the conditioning variable. The best-fitted vine structure was selected using goodness-of-fit (GOF) test statistics. The performance of the nonparametric vine approach was also compared with those of vines constructed with a parametric and semiparametric fitting procedure. Investigation revealed that the D-vine copula constructed using a Bernstein copula with normal KDE marginals performed well nonparametrically in capturing the dependence of the compound events. Finally, the derived nonparametric model was used in the estimation of trivariate joint return periods, and further employed in estimating failure probability statistics.

Reference evapotranspiration estimation in hyper-arid regions via D-vine copula based-quantile regression and comparison with empirical approaches and machine learning models

Study regionTwo hyper-arid regions (Atbara and Kassala stations) in Sudan. Study focusThe study aims to evaluate the potential of the D-vine Copula-based quantile regression (DVQR) model for estimating daily ETo during 2000–2015 based on various input structures. Further, the DVQR model was compared with Multivariate Linear quantile regression (MLQR), Bayesians Model Averaging quantile regression (BMAQR), Empirical Models (EMMs), and Classical Machine Learning (CML). Besides, the CML models including Random Forest (RF), Support Vector Machine (SVM), Extreme Learning Machine (ELM), Extreme Gradient Boosting (XGBoost), and M5 Model Tree (M5Tree) were employed. New hydrological insights for the regionThe original EMMs showed poor performance, which improved after calibration techniques. The DVQR, MLQR, and BMAQR models showed better performance than the calibrated EMMs. However, the DVQR model exhibited the highest accuracy than the MLQR and BMAQR models over two study sites. The M5Tree, SVM, and XGBoost models perfumed better than ELM and RF models at both study sites. The DVQR and XGBoost models showed equivalent performance (R2, NSE, and WIA > 0.99, MAE, and RMSE < 0.2) to the M5Tree and SVM models, but they had significantly more accuracy than the calibrated EMMs, MLQR, BMAQR, ELM, and RF models in two hyper-arid regions. Overall, the high dimensional DVQR model is recommended as a promising alternative technique for estimating daily ETo in hyper-arid climate conditions around the world.

Reliability estimation of complex systems based on a Wiener process with random effects and D-vine copulas

Random effects are ubiquitous in the degradation processes of multiple performance characteristics (PCs) of a complex system, and these PCs are not commonly independent. Neglecting either of the above features will lead to bias in system reliability estimation. Therefore, this study develops a reliability estimation method for the complex systems with multiple PC degradations considering both of the features. First, a Wiener process-based marginal degradation model with random effects (including the random initial PC, unit-to-unit variability, temporal uncertainty, and measurement errors) is proposed to track the degradation path of each PC. A model based on D-vine copulas is put forward to describe the correlation among multiple PCs. Then, a system reliability function is derived based on the two models. Furthermore, a two-step statistical inference is developed to estimate the unknown parameters in the system reliability function. Finally, using a practical case, the effectiveness of the proposed method is illustrated.

A Novel Uncertainty Quantification Framework for PF and OPF Considering Nonlinear Correlated Power Injections With Limited Information

This paper proposes a new uncertainty quantification framework for power flow (PF) and optimal power flow (OPF) considering the nonlinear correlations of uncertain power injections with limited information. The D-Vine copula is leveraged to capture the nonlinear correlations among uncertain power injections from historical data. This is further integrated with the evidence theory and the reformulated quadratic affine form to obtain PF and OPF results. The D-Vine copula and evidence theory allow one to effectively eliminate the explosive-growth joint focal elements of large-scale power system with large numbers of partial known uncertain power injections, leading to significant reduction of computing time. The reformulated quadratic affine form aims at characterizing the PF and OPF outputs with partially known uncertain power injections in a simple form based on Dempster-Shafer structure, yielding further computational efficiency improvement without the loss of accuracy. Comparison results with other alternatives show that the proposed framework leads to more accurate PF and OPF outcomes while achieving high computational efficiency for large-scale power systems with large numbers of nonlinear correlated power injections in presence of limited information.