Vine Copula Research Articles

Multivariate probability analysis of wind-wave actions on offshore wind turbine via copula-based analysis

Floating structures in service encounter extreme natural hazards, such as correlated extreme wind-wave loads. This study aims to provide realistic multivariate models of environmental parameters to accurately describe the statistical characteristics of metoceanic conditions, which are essential for the reliability-based design of marine structures. The multiload analysis method includes three major steps: (1) to identify the best-fit univariate marginal distributions of the wind-wave parameters. Mixed models composed of a set of single-mode parametric distributions were found to be more suitable for the measured variables. (2) To construct joint probability distributions of multiple variables using copula-based models, the performance of various models namely, trivariate metaelliptical copulas, Archimedean copulas, and vine copula models. It was observed that joint distributions can be best modelled using vine copula models with considerable flexibility. The final process involves establishing environmental surfaces and contours based on the inverse first-order reliability method. The most unfavourable combination of extreme design conditions can be defined on the environmental surface which is useful for evaluating the response characteristics of offshore wind turbines. These expressions provide a preliminary assessment of wind-wave loads on offshore structures.

The negative-positive feedback transition thresholds of meteorological drought in response to agricultural drought and their dynamics

There are complex bidirectional feedback relationships among different types of droughts (e.g., meteorological and agricultural droughts). As agricultural drought intensifies, meteorological drought response to agricultural drought may be changed from negative to positive feedback. Nevertheless, the negative-positive feedback transition thresholds of meteorological drought in response to agricultural drought and their dynamics have remained unsolved. Herein, we proposed a new quantitative method to characterize the mutual feedback between meteorological drought and agricultural drought based on the vine copula function for the first time in this study. The negative-positive feedback transition threshold and the sensitivity of the feedback were quantified under certain drought conditions. In order to investigate the feedback relationship dynamics under a changing environment, the total study period was evenly divided into two stages: stage 1 (1982–1999) and stage 2 (2000–2018). Finally, the random forest method was used to explore the dominant factors on the transition threshold. Results indicate that: (1) the negative-positive feedback transition thresholds in August is generally lower than June and July in mainland China, the basin with large threshold is the Southwest River Basin; (2) the sensitivity of meteorological drought in response to agricultural drought was higher in positive feedback than in negative feedback; (3) the transition thresholds of stage 2 was mostly reduced, while the feedback sensitivity of positive feedback was mostly increased; and (4) compared with the single factor, the land-meteorological coupling strength (the correlation between precipitation and soil moisture) dominants the negative-positive feedback transition threshold. This study sheds new insights into droughts feedback.

The impact of Federal Reserve Interest Rate Hikes on the Systemic Risk of the U.S. Banking Industry: Based on Semi-Parametric Vine Copula SCCA Model

We use the Vine Copula SCCA model to measure the systemic risk of the US banking industry, and compares the impact of two different events, external risk and Fed rate hike on systemic risk. The results demonstrate that the systemic risk of the US banking industry reached its peak when affected by external shocks (2020) but was quickly released by market rescue measures. When the Fed raised interest rates consecutively in 2022, large banks showed good resistance to risk, but the joint default risk of small and medium-sized banks remained at a significant level for a long time, indicating that interest rate hikes may have increased the systemic risk of the US banking industry. US banking industry should maintain good risk management and prudent operation, and the regulatory intensity they receive also needs to be strengthened.

Aerospace structural reliability analysis method based on regular vine copula model with the asymmetric tail correlation

Considering the asymmetric tail correlations between variables in reliability analysis, an effective aerospace structural reliability analysis method based on regular vine copula models is proposed. Firstly, a product of multiple pair-copula functions and marginal density functions based on regular vine copula models are used to construct the joint probability density function. Secondly, the asymmetric copula functions are introduced into the candidate construction sets of pair-copula functions for capturing asymmetric tail correlations between variables. Meanwhile, the akaike information criterion (AIC) is adopted to select the optimal pair-copula functions. Thirdly, taking the difference of multi-dimensional correlations into account, six different regular vine copula models are used to construct the multivariate joint probability density function. And the corresponding regular vine copula-first order reliability method (RVC-FORM) considering the asymmetric tail correlation is proposed. Finally, three numerical examples and an aerospace turbine blade example are investigated to demonstrate the validity of the proposed method.

Portfolio optimization through hybrid deep learning and genetic algorithms vine Copula-GARCH-EVT-CVaR model

This study investigates the potential benefits of using the Conditional Value at Risk (CVaR) portfolio optimization approach with a GARCH model, Extreme Value Theory (EVT), and Vine Copula to obtain the optimal allocation decision for a portfolio consisting of Bitcoin, gold, oil, and stock indices. First, we fit a suitable GARCH model to the return series for each asset, followed by employing the Generalized Pareto Distribution (GPD) to model the innovation tails. Next, we construct a Vine Copula-GARCH-EVT model to capture the interdependence structure between the assets. To refine risk assessment, we combine our model with a Monte Carlo simulation and Mean-CVaR model to optimize the portfolio. In addition, we utilize a novel version of deep machine learning's genetic algorithm to address the optimization decision. This research contributes new evidence to the CVaR portfolio optimization approach and provides insights for portfolio managers seeking to optimize multi-asset portfolios.

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.

Development of decomposition-based model using Copula-GARCH approach to simulate instantaneous peak discharge

Estimation of instantaneous peak discharge is important in the design of hydraulic structures and reservoir management. In this study, a new approach called CEEMD-Copula-GARCH is presented for simulating instantaneous peak discharge in the Qale Shahrokh basin, upstream of Zayanderood Dam, Iran. In the developed method, the Complementary ensemble empirical mode decomposition (CEEMD) algorithm was used to analyze the observed values and generate the intrinsic mode function values and residual series. For this purpose, the intrinsic mode function values were simulated based on vine copula and its tree sequence (C-vine, D-vine, R-vine and their independent and Gaussian modes), and the residual series of the CEEMD algorithm were simulated by the GARCH model. The results of simulating instantaneous peak discharge values (m3/s) using the CEEMD-Copula-GARCH approach in the study area showed that the amount of simulation error based on the RMSE statistic compared to the CEEMD-Copula model and simulation without decomposition has improved by about 20 and 70%, respectively. The model’s efficiency was also estimated based on the Nash–Sutcliffe efficiency in the proposed approach of 0.99, and the certainty of the proposed approach was also confirmed based on the presented violin plot. According to the presented results, the proposed approach has high accuracy and efficiency in the simulation of instantaneous peak discharge (m3/s), which can be used in the flood control system design and flood management. Using the methodology proposed in this study, multivariable models can be used in simulating univariate series with high accuracy.

An Intelligent Risk Forewarning Method for Operation of Power System Considering Multi-Region Extreme Weather Correlation

Extreme weather events pose significant risks to power systems, necessitating effective risk forewarning and management strategies. A few existing researches have concerned the correlation of the extreme weather in different regions of power system, and traditional operation risk assessment methods gradually cannot satisfy real-time requirements. This motivates us to present an intelligent risk forewarning method for the operation of power systems considering multi-region extreme weather correlation. Firstly, a novel multi-region extreme weather correlation model based on vine copula is developed. Then, a risk level classification method for power system operations is introduced. Further, an intelligent risk forewarning model for power system operations is proposed. This model effectively integrates the multi-region extreme weather correlation and the risk level classification of the system. By employing the summation wavelet extreme learning machine, real-time monitoring and risk forewarning of the system’s operational status are achieved. Simulation results show that the proposed method can rapidly identify potential risks and provides timely risk forewarning information, helping enhance the resilience of power system operations.

Efficient quantification of composite spatial variability: A multiscale framework that captures intercorrelation

Composite structures suffer from material imperfections. Non-deterministic models at the micro- and mesoscale propagate this spatial variability. However, they become impractical when the structure size increases. This paper proposes a numerically efficient multiscale methodology that links structural behaviour with the spatial variability of material imperfections on smaller scales. Fibre strength variability is accounted for through a fibre break model. A mesoscale model considers fibre volume fraction and fibre misalignment variability using random fields. Measurements provide probabilistic data for these imperfections. Subsequent homogenisation results in intercorrelated material properties on the structural macroscale that are modelled effectively with vine copulas. The methodology is verified by predicting the failure load of a coupon model. Predictions are very similar to those obtained by directly modelling spatial variability on the structural scale.

Improving Bayesian Classifier Using Vine Copula and Fuzzy Clustering Technique

Improving Bayesian Classifier Using Vine Copula and Fuzzy Clustering Technique

Extreme risk spillovers between China and major international stock markets

We examine the complex dependence structure and risk spillovers between the Chinese stock market and twelve major international markets. To this end, we employ three types of vine copulas and tests for the Granger causality in risk of Hong et al. (2009). The results indicate that the R-vine copula is the optimal model to characterize the high-dimensional dependence structure of the markets after China joined the WTO, which suggests obvious structural differences with varying degrees of mainly positive dependences. Moreover, we identify unilateral extreme risk spillovers from China to the United States, France, and Germany, and either from Japan to China. We also detect bilateral spillovers between China and the United States, Japan, as well as Australia.

Storm CAT Bond: Modeling and Valuation

The frequency and intensity of weather-related catastrophes, such as storms and floods, have been increasing due to climate change. This leads to rising storm catastrophe risks to the property–casualty insurance and reinsurance sector. In this article, we propose an index-based storm catastrophe (CAT) bond for reinsurers to hedge catastrophe risks related to storm losses. Storm loss data have a large portion of zero values and a continuous positive right-skewed distribution, together with high-dimensional spatial dependence. We address these unique properties by proposing a general two-part autoregressive (2PAR) distribution as the marginal model and a semicontinuous spatiotemporal vine copula as the dependence model. We investigate the CAT bond market equilibrium and endogenously solve for the optimal market price of risk and coupon rates. Our empirical results using historical loss data at the county level in Florida show that the proposed CAT bond can stabilize the reinsurer’s cash flows and create attractive returns to investors by offering high coupon rates. Our framework can be generalized to design and price other catastrophe financing facilities.

Vine Copula based Portfolio Level Conditional Risk Measure Forecasting

Accurately estimating risk measures for financial portfolios and validating their robustness is critical for both financial institutions and regulators. However, many existing models operate at the aggregate portfolio level, hence they fail to capture the complex cross-dependencies between portfolio components and particularly provide no methodology to perform a sensitivity analysis on the estimates. To address both aspects, a new approach is presented that uses vine copulas in combination with univariate ARMA-GARCH models for marginal modelling to compute conditional portfolio-level risk measure estimates by simulating portfolio-level forecasts conditioned on a stress factor. A quantile-based approach is then presented to observe the behaviour of risk measures given a particular state of the conditioning asset(s). In an illustrative case study of Spanish equities with different stress factors, the results show that the portfolio is quite robust to a sharp downturn in the American market. At the same time, there is no evidence of this behaviour with respect to the European market. The novel algorithms presented are ready for use through the R package portvine, which is publicly available on CRAN.

A Framework of Dependence Modeling and Evaluation System for Compound Flood Events

AbstractThe coincidence and superposition of flood processes from different rivers and regions tend to form compound flood events, determined by spatial relationship between diverse flood processes that cannot be accurately depicted and evaluated by existing dependence analysis methods. A framework, integrating multi‐dimensional vine copula model and dependence evaluation system, was developed with a testing‐oriented application to explore underlying dependence between two kinds of extreme runoff series (peak discharge and flood volume) extracted from the identified compound flood events in the upper reaches of the Yangtze River. Multi‐dimensional regular vine (R‐vine) copula models were established to depict the complex and diverse dependence, and corresponding vine structure was specified by the vine structure array that can reflect the sequence of tributaries flowing into the main stream and the spatial locations of different hydrometric stations. Dependence magnitude and association status were calculated and compared according to the optimal R‐vine copula models and information theory. Comparison with existing methods demonstrated that dependence evaluation system could reflect nonlinear and local dependence characteristics and eliminate the effect of extreme runoff series from other hydrometric station on the dependence. The association status between different extreme runoff series of the upper Yangtze River and its tributaries were diverse in view of the impact of tributary flood inflow. The proposed framework can be regarded as an effective way for dependence modeling and evaluation of compound floods, thus providing a scientific reference for the risk analysis of water resources systems.

Emergency Power Supply Restoration Strategy for Distribution Network Considering Support of Microgrids with High-Dimensional Dynamic Correlations

With the rapid development of renewable energy, microgrids are becoming more and more essential in distribution networks. However, uncertainties brought by new energy sources have posed great challenges to the energy safety and stability of distribution networks, especially in the process of fault restoration. To address these issues, this paper investigates an emergency power supply recovery strategy for distribution networks by considering the support capability of microgrids and the high-dimensional dynamic correlations of uncertainty. Firstly, the structure of distribution networks including microgrids is analyzed. Then, the high-dimensional dynamic vine copula model is proposed to model the joint output uncertainty process. Next, island partition and operation models are established, including the objective function and constraint conditions, and the model solving methods are also presented. Finally, an example analysis is conducted to verify the effectiveness of the proposed strategy. The results show that the proposed strategy is able to deal with the uncertainties brought by renewable energy sources in distribution networks with microgrid support, improving energy safety and stability. This research provides valuable insights for the development of emergency power supply strategies in distribution networks.

Stochastic optimal scheduling strategy for a campus-isolated microgrid energy management system considering dependencies

Isolated microgrids have been widely used on campuses, becoming an important part of their power-supply infrastructure. In this study, a stochastic optimal scheduling strategy that considered dependencies was proposed for the energy management system (EMS) of an isolated microgrid on campus, which consists of three main components: an accurate forecasting model on both the demand and supply sides, an excellent core scheduling strategy, and an effective uncertainty analysis. First, the forecasting model involved data correction, feature selection, core forecasting, and error analyses to obtain consistently good forecasting results. A multilayer hybrid forecasting model was developed, including a stacked multilevel denoising autoencoder, mutual information, bidirectional long short-term memory network (LSTM), and LSTM, corresponding to the above four model elements. Based on the forecasting results, improved episodic deep reinforcement learning was used to build a stochastic optimal scheduling strategy for the EMS, which could realize rapid propagation of reward values and achieve stable updating of episodic memory, effectively improving sample efficiency. The objective of optimizing the scheduling was to obtain the lowest operational cost. Finally, the uncertainties in the forecasting process were analyzed using the Latin hypercube sampling method, and a regular vine copula was used to determine the dependence of the uncertainty analysis between buildings. To the best of our knowledge, this is the first study to consider dependence in the uncertainty analysis of a campus microgrid. The performance of the proposed method was evaluated by comparing it with other existing models, aiming to obtain more efficient and stable scheduling results.

Portfolio optimization based on forecasting models using vine copulas: An empirical assessment for global financial crises

AbstractWe employ and examine vine copulas in modeling symmetric and asymmetric dependency structures and forecasting financial returns from 2001 to 2022, a period that includes the 2008 financial crisis, the 2011 European sovereign debt crisis, the 2020 COVID‐19 pandemic crisis, and the 2022 Russian invasion of Ukraine with the resulting energy crisis. We analyze the asset allocations performed and test different portfolio strategies, such as maximum Sharpe ratio, minimum variance, and minimum conditional value at risk. Using international financial market indices, we specify the regular, drawable, and canonical vine copulas, such as the Gaussian, Student's , Clayton, Frank, Joe, Gumbel, and mixed copulas, and analyze both in‐sample and out‐of‐sample portfolio performances. Out‐of‐sample portfolio back‐testing shows that vine copulas reduce portfolio risk better than the benchmark portfolio strategies and also better than simple multivariate copulas. Overall, we find that mixed vine copula models perform best with regard to risk reduction, both for the entire period 2001–2022 and during financial crises periods. Thus, a mixture of symmetric and asymmetric copula families works best in terms of portfolio risk reduction irrespective of the chosen optimization approach.

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.

How does bubble risk propagate among financial assets? A perspective from the BSADF-vine copula model

In this paper, the BSADF method is used to construct the bubble net value sequence of 11 mainstream financial assets, and the vine copula model is used to analyze the characteristics of the bubble-related structure. First, we use the BSADF method to measure the bubbles of various financial assets. The results show that since the outbreak of COVID-19, most types of assets have experienced a sharp bubble rise and their longest bubble period as central banks have implemented quantitative easing policies. Furthermore, this article reveals the path characteristics of bubble risk transmission in different assets using the vine copula model. The R vine copula is found to be best for analyzing the tail dependence structure. The S&P 500 and the international gold price occupy the hub position in the bubble dependence structure of various financial assets. The Shanghai Composite Index and the US Dollar Index can act as relays and accelerators in the transmission of bubble risk across the financial system. Finally, we explore the tail dependence structure between financial assets. The results indicate that gold can be a good hedge against the bubble risk of the Hang Seng Index and WTI crude oil futures. The COVID-19 pandemic and accommodative monetary policies by governments can create conditions for bubble risk to spread between assets such as Bitcoin and China’s 10-year Treasury bonds and between the US Dollar Index and the S&P 500.

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.