R-vine Copula Research Articles

An R-vine copula analysis of non-ferrous metal futures with application in Value-at-Risk forecasting

We employ the R-vine copula approach to study the dependence structure between non-ferrous metal commodity futures on the London Metal Exchange, focusing on the comparison before and after structural breaks. We find that the center of the dependence structure between non-ferrous metal futures shifts from copper to zinc after the first structural break in 2008 and moves back to copper after the second structural break in 2014. Additionally, we document that non-ferrous metals experienced an increase in the level of integration and tail dependence between 2008 and 2014, while this increase is shown to cease after 2014. We further develop an R-vine copula-based method for forecasting Value-at-Risk, and the backtesting results show superior forecasting accuracy over the benchmark methods. Our study is useful for market participants seeking to enhance their risk management for non-ferrous metals.

Has the dependence structure of the BRICS exchange rates changed after the financial crisis? Evidence from R-Vine copula model

PurposeThe authors examine the dependence structure of the BRICS exchange rates.Design/methodology/approachThe authors construct a regular vine copula model to study the co-movements of exchange rates in BRICS controlling the influences from the SDR currencies and the oil prices.FindingsThe main findings show that, after the financial crisis, RMB pursued a more balanced strategy shifting from USD-centered to USD-EUR dependency and the oil prices become more dependent on RUB than USD, which could weaken the dollar hegemony. From robustness tests, we find that the inclusion of RMB in SDR has certain but limited impacts on the dependence structure and the influence of the GBP weakened as well. The results have important implications for currency trade, policy design and the future of the BRICS.Originality/valueThe contribution of this paper is twofold. First, we examine the interdependence structure of the BRICS exchange rates controlling for the influence of SDR currencies and the oil prices with R-Vine copula model. Second, we compare the pre- and after-crisis structure and see if the financial crisis and the BRICS summits have changed the structure.

Re-examination of international bond market dependence: Evidence from a pair copula approach

The finance literature provides substantial evidence on the dependence between international bond markets across developed and emerging countries. Early works in this area were based on linear models and multivariate GARCH models. However, based on the limitations of these models this paper re-examines the non-linearity, multivariate and tail dependence structure between government bond markets of the US, UK, Japan, Germany, Canada, France, Italy, Australia and the Eurozone, from January 1970 to February 2019 using ARMA-GARCH based pair- copula models. We find that the bond markets in our sample tend to have both upper tail dependence in terms of positive shocks and lower tail dependence in terms of negative shocks. The estimated C-vine shows Eurozone has the highest average dependency. The D-vine, with optimal chain dependency structure shows the best order of connectedness to be the UK, the USA, Italy, Japan, Eurozone, France, Canada, Germany and Australia. The R-vine copula results underline the complex dynamics of bond market relations existing between the selected economies. The estimated R-vine shows Eurozone, Germany and Australia are the most inter-connected nodes. The multivariate distribution structure (interdependency) of bond markets for all countries were modelled with the C-vine, D-vine and R-vine copulas. In this application, the R-vine copula allows for detailed modelling of all bond markets and hence provides a more accurate goodness of fit and mean square error for the interdependency between all markets. In light of the changing volatility in bond markets, we conduct additional tests using time-varying copulas and find that the dependence structure among the bond markets examined is time-varying with the dynamic dependence parameter plots revealing that the nature of the dependence structure is intense during crisis periods.

An application of Regular Vine copula in portfolio risk forecasting: evidence from Istanbul stock exchange

<abstract> In times of financial turbulence, it is a well-documented fact that the co-movement of financial returns tends to increase leading to unexpected portfolio losses. The magnitude of the losses can severely be underestimated when the characteristics of univariate return series and the dependence structure between the returns are not represented well by a risk forecasting model. From a growing literature on the available multivariate modelling tools, this paper aims to investigate daily portfolio Value at Risk and Expected Shortfall forecasting performance of elliptical as well as Regular Vine copulas. For this purpose, return series of twelve stocks that are listed in Istanbul Stock Exchange are obtained for the period of June 2010 to December 2018. The series are modelled with univariate Generalized Auto-Regressive Conditional Heteroskedasticity models with Normal and Student's t innovations. Equally weighted portfolio returns are forecasted depending on the univariate GARCH marginals and their multivariate dependence structure. Estimated daily portfolio Value at Risk and Expected Shortfall values with varying levels are compared with the traditional Variance-Covariance and Dynamic Conditional Correlation Multivariate GARCH model estimates. While the models performed well at the Value at Risk backtests, according to the applied ES backtests R-vine copula GARCH found better at yielding more accurate Expected Shortfall forecasts. </abstract>

Correlation modeling of multiple wind farms based on piecewise cloud representation and regular vine copulas

The accuracy of correlation modeling for multiple wind farms will directly affect the assessment results of absorption capacity in electric utilities. Due to the rapid increase in installed capacity of wind power in recent years, there are often multiple wind farms with complex correlations in a region, and traditional correlation models are inaccurate and highly computational. In order to enhance the accuracy of correlation modeling for multiple wind farms, this paper combines the piecewise cloud representation and regular vine (R-vine) copulas for classification modeling purposes. The piecewise cloud representation is used to divide the multiple wind farms’ data into different categories, and the correlation models of different categories are established based on the R-vine copulas. A case of the SCADA system record data of 6 wind farms in Northwest China has been adopted to evaluate the effectiveness compared with its competitors. Case studies have demonstrated that the proposed method not only has good performances on modeling the correlation better than the traditional method but also has strong robustness, especially in the case that the correlation of different wind farms is inconsistent. Most importantly, this model is able to extract the correlations of different features in multiple wind farms’ data and then targeted modeling.

Probabilistic power forecast of renewable distributed generation for provision of control reserve using vine copulas

This work focuses on calculating the amount of control reserve, which can be provided by a pool of renewable power plants on the next day. The power forecast of wind and solar power plants depends on the weather forecast, which always contains errors. A merger of individual plants at different locations is advantageous in order to reduce the overall forecast error. Still, the amount of control reserve needs to be determined with a high level of reliability. For the calculation, a probabilistic approach based on historical and current weather data is chosen. In order to model the spatial dependencies of the forecast errors between individual plants, R-vine copulas are used. In the copula theory, R-vine copulas provide high accuracy in modelling the dependency of stochastic variables. The methodology is validated and compared to three alternative approaches with a use case of 32 wind and solar plants. The calculated amount of control reserve provided and the achieved reliability proves to be superior to alternative approaches. Additionally, the required reliability level is varied to investigate the impact on the amount of control reserve, which can be offered with the pool.

Robust Omega ratio optimization using regular vines

We study the robust portfolio optimization model for the Omega ratio when the joint ambiguity in the returns distributions is modeled utilizing copulas. We propose the copula formulation of the Omega ratio and use it to formulate the worst-case robust optimization model. Furthermore, we propose a Markov chain predicated filtering strategy to filter a set of fewer assets from a large pool of available assets in the market to amend the performance of the conventional Omega ratio model. We propose an R-vine copula Autoregressive Moving Average Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) model for the joint distribution of assets returns. We obtain the standardized residuals for each return series of the filtered assets using the ARMA-GARCH model and, subsequently, exploit the regular vine copulas to model the joint dependence among the transformed residuals. The tree structure in the regular vines is accomplished using Kendall’s tau. The dependence structure so obtained is used to simulate scenarios for the returns of assets. The simulated data is used to obtain optimal portfolios in the worst-case Copula Omega ratio model. Empirical evidence shows the aptness of the proposed filtering strategy and analyzes the performance of the worst-case copula Omega portfolios on several datasets using a rolling window approach. The optimal portfolios from the worst-case copula Omega model are found to outperform the portfolios from the Gaussian copula Omega ratio model by having a higher information ratio, Value-at-risk ratio, and Rachev ratio.

Reservoir Inflow Synchronization Analysis for Four Reservoirs on a Mainstream and its Tributaries in Flood Season Based on a Multivariate Copula Model

To meet flood control demand, many reservoirs have been built successively in China for many years. Reservoir inflow synchronization analysis for multiple reservoirs in the flood season can provide a reference for the formulation of the joint water supply operation plan and improve the utilization efficiency of water resources. In this paper, a two-dimensional copula model is used to analyze the reservoir inflow synchronization between a single reservoir on a tributary and the reservoir on the mainstream of the river in the flood season. Based on the obtained results, a R-vine copula model is established by selecting a suitable structure to analyze the multidimensional joint reservoir inflow synchronization for multiple reservoirs in the middle and lower reaches of the Yellow River basin in the flood season. For four selected reservoirs in the middle and lower reaches of the Yellow River basin in China as a case study, the frequencies of synchronous wetness and synchronous dryness for the four reservoirs are 15.106% and 15.209%, respectively. The research results can serve as a reference for actual scheduling.

A R-Vine Copula Analysis of Non-ferrous Metal Futures with Application in Forecasting Value-at-Risk

We employ the R-vine copula approach to study the dependence structures among non-ferrous metal commodity futures on the London Metal Exchange, focusing on the comparison before and after the 2008 financial crisis. We document that the center of dependence structure among non-ferrous metal futures has changed from copper to zinc after the crisis. We find that the risk diversification benefit among non-ferrous metals diminishes after the crisis, and there is a significantly increase in their tail dependence. We further develop a R-vine copula-based method for forecasting Value-at-Risk, and the back-testing results show superior forecast accuracy over benchmark methods. Our study is useful for market participants to enhance their risk management for non-ferrous metals.

Research on Information Spillover Effect of the RMB Exchange Rate and Stock Market Based on R-Vine Copula

This paper studies the dependence structure and information spillover effect between the RMB exchange rate and the Chinese stock market based on the R-vine copula model and spillover index model. The results show that due to the occurrence of the trade war, the correlation between the three RMB exchange rate indicators and the two stock market indicators increases in varying degrees. In the intensity of spillover, the information spillover of the stock market to the RMB exchange rate is significantly enhanced, and the information spillover intensity of the RMB Index to the stock market increases, but the information spillover of the US dollar and Hong Kong dollar exchange rates to the stock market is significantly weakened. In the direction of spillover, the spillover of the RMB Index and stock market shows the characteristics of alternating transformation, while the exchange rate of a single currency and the stock market shows a one-way transmission from the stock market to the exchange rate. Additionally, the information spillover between the RMB exchange rate and the stock market is closely related to the degree of market openness. The RMB Index contains more information than the exchange rate of a single currency.

Robust Portfolio Selection with Regime Switching R-Vine Copulas

This paper solves the portfolio selection problem with regime switching and asymmetric dependence in financial markets. Investors sustain substantial loss in times of crisis and expect to reduce their losses. Thus, we consider the uncertainty in hidden states of the economy and define worst-case conditional value-at-risk (WCVaR) to capture extreme portfolio loss during financial crisis. Then, we formulate the portfolio selection problem with WCVaR as the measure of risk. We conduct an empirical study using 13 global equity indices. The results show that for dynamic investments, or during financial crisis, our model outperforms other models that only consider a fixed dependence structure between assets. This is because our model can significantly reduce extreme portfolio loss in times of crisis by selecting the assets with small lower tail dependence. This new portfolio strategy can help risk-averse investors cope with financial crisis.

Vine copula selection using mutual information for hydrological dependence modeling

Hydrological risk analysis and management entails multivariate modeling which requires modeling the structure of dependence among different variables. Vine copulas have been increasing applied in multivariate modeling wherein the selection of vine copula structure plays a critical role. Inspired by the relationship between Mutual information (MI) and copula entropy (CE), this study discussed the connection between conditional mutual information (CMI) and CE and developed a mutual information-based sequential approach to select a vine structure which was based on original observations, and model-independent. Then, to reduce the complexity of R-vine copulas, a statistical method-based truncation procedure was applied. Finally, an MI-based approach for hydrological dependence modeling was developed. Two types of hydrological processes with different dependence structures were utilized to show the performance of the proposed approach: (i) drought characterization: showing a D-vine structure; and (ii) multi-site streamflow dependence: showing a C-vine structure. Results indicated that the MI-based approach satisfactorily modeled different kinds of dependence structure and yielded more information on variables in comparison with traditional tau-based approach.

A Markov-switching COGARCH approach to cryptocurrency portfolio selection and optimization

Blockchain is a new technology slowly integrating our economy with cryptocurrencies such as Bitcoin and many more applications. Bitcoin and other versions of it (known as Altcoins) are traded everyday at various cryptocurrency exchanges and have drawn the interest of many investors. These new types of assets are characterized by wild swings in prices, and this can lead to large swings in profit and losses. To respond to these dynamics, cryptoinvestors need adequate tools to guide them through their choice of portfolio selection and optimization. Bitcoin returns have shown some form of regime change, suggesting that regime-switching models could more adequately capture the volatility dynamics. This paper presents a two-state Markov-switching COGARCH-R-vine (MSCOGARCH) model for cryptocurrency portfolio selection and compares the performance to the single-regime COGARCH-R-vine (COGARCH). The findings here are in line with the literature where MSCOGARCH outperforms the single-regime COGARCH with regard to the expected shortfall risk. The COGARCH specifications here capture the structural breaks and heavy tailness within each state of the Markov switching in order to achieve a minimal risk and a maximum return. The flexibility of R-vine copula allows adequate bivariate copula selection for each pair of cryptocurrencies to achieve suitable dependence structure through pair-copula construction architecture.

Forecasted Scenarios of Regional Wind Farms Based on Regular Vine Copulas

Owing to the uncertainty and volatility of wind energy, forecasted wind power scenarios with proper spatio-temporal correlations are needed in various decision-making problems involving power systems. In this study, forecasted scenarios are generated from an estimated multi-variate distribution of multiple regional wind farms. According to the theory of copulas, marginal distributions and the dependence structure of multi-variate distribution are modeled through the proposed distance-weighted kernel density estimation method and the regular vine (R-vine) copula, respectively. Owing to the flexibility of decomposing correlations of high dimensions into different types of pair-copulas, the R-vine copula provides more accurate results in describing the complicated dependence of wind power. In the case of 26 wind farms located in East China, high-quality forecasted scenarios as well as the corresponding probabilistic forecasting and point forecasting results are obtained using the proposed method, and the results are evaluated using a comprehensive verification framework.

Robust Portfolio Selection Using Vine Copulas

Portfolio optimization problems involving Conditional Value-at-Risk (CVaR) are often computationally intractable and require complete information about the distribution of returns, which is rarely available in practice. These difficulties are compounded when the portfolio contains a lot of assets. In this paper, we consider the worst-case CVaR (WCVaR) under mixture of vine copulas distribution uncertainty, which can capture complex and hidden dependence patterns in multivariate data.We compare the out-of-sample performance of the robust strategies based on the mixture of R-vine copulas, mixture of C-vine copulas, mixture of D-vine copulas and nominal CVaR method. The experimental study shows that the robust models based on mixture of R-Vine copulas and mixture of C-Vine copulas perform the best in terms of average returns, Sharpe ratio and cumulative returns. The performance of robust mixture of D-Vine copulas model might be advantageous when the correlation between assets is low.

Dependence risk analysis in energy, agricultural and precious metals commodities: a pair vine copula approach

ABSTRACT We apply pair vine copulas, specifically the C-vine and R-vine copulas, to examine the conditional multivariate dependence pattern/structure and R-vine copula-based value-at-risk (VaR) to assess financial portfolio risk. We examine the co-dependencies of 13 major commodity markets (which include three energy commodities, six agricultural commodities and four precious metals prices) from 2 January 2003 to 19 December 2016. Dividing our sample into three sub-periods, namely pre-GFC, GFC and post-GFC, we find that the dependencies among commodities undergo changes in a complex manner, changing in different financial conditions, and that the Student-t copula appears on the maximum number of occasions, especially during the GFC period, signifying the existence of fatter tails in the distributions of returns. We further show that the co-dependencies computed using R-vine copulas are best suited to compute the portfolio VaR during the considered time period.

A Vine Copula-Based Hierarchical Framework for Multiscale Uncertainty Analysis

Abstract Uncertainty analysis is an effective methodology to acquire the variability of composite material properties. However, it is hard to apply hierarchical multiscale uncertainty analysis to the complex composite materials due to both quantification and propagation difficulties. In this paper, a novel hierarchical framework combined R-vine copula with sparse polynomial chaos expansions is proposed to handle multiscale uncertainty analysis problems. According to the strength of correlations, two different strategies are proposed to complete the uncertainty quantification and propagation. If the variables are weakly correlated or mutually independent, Rosenblatt transformation is used directly to transform non-normal distributions into the standard normal distributions. If the variables are strongly correlated, the multidimensional joint distribution is obtained by constructing R-vine copula, and Rosenblatt transformation is adopted to generalize independent standard variables. Then, the sparse polynomial chaos expansion is used to acquire the uncertainties of outputs with relatively few samples. The statistical moments of those variables that act as the inputs of next upscaling model can be gained analytically and easily by the polynomials. The analysis process of the proposed hierarchical framework is verified by the application of a 3D woven composite material system. Results show that the multidimensional correlations are modeled accurately by the R-vine copula functions, and thus uncertainty propagations with the transformed variables can be done to obtain the computational results with consideration of uncertainties accurately and efficiently.

An R-Vine Copula Based Control Chart for Monitoring Multivariable and Mixed-type Data

多维混合型数据监测问题一直是质量控制和质量管理中的重点和难点。混合型数据包括名义型、顺序型和数值型3种类型。传统的多变量控制图往往只考虑数值型的数据，在应用中存在一定的局限性。同时，在实际场景中，各类变量之间往往存在一定的相关性，这也是在传统控制图中容易被忽略的关键点。本文通过引入Copula-Vine模型，充分利用了顺序型变量的秩相关性，建立了一种新的基于R-Vine Copula的混合型数据控制图(R-Vine Copula control chart, RVC)。通过算例比较，验证了该控制图相对于现有模型在混合型数据监测方面更强的灵活性和有效性。

Detecting contagion in Asian exchange rate markets using asymmetric DCC-GARCH and R-vine copulas

This study uses asymmetric DCC-GARCH models and copula functions to study exchange rate contagion in a group of twelve Asia-Pacific countries. Using daily data between November 1991 and March 2017, we show that extreme market movements are mainly associated with the high degree of interdependence registered by countries in this region. Evidence of contagion is scarce. Asymmetries do not appear to be important. Specifically, currency co-movements are statistically identical during times of extreme market appreciation and depreciation, indicating that phenomena such as the fear of “appreciation” do not appear to be relevant in the region’s foreign exchange markets.

Probabilistic Peak Load Estimation in Smart Cities Using Smart Meter Data

Adequate capacity planning of substations and feeders primarily depends on an accurate estimation of the future peak electricity demand. Traditional coincident peak demand estimation is carried out based on the empirical metric, after diversity maximum demand, indicating individual peak consumption levels and demand diversification across multiple residents. With the privilege of smart meters in smart cities, this paper proposes a data-driven probabilistic peak demand estimation framework using fine-grained smart meter data and sociodemographic data of the consumers, which drive fundamental electricity consumptions across different categories. In particular, four main stages are integrated in the proposed approach: load modeling and sampling via the proposed variable truncated R-vine copulas method, correlation-based customer grouping, probabilistic normalized maximum diversified demand estimation, and probabilistic peak demand estimation for new customers. Numerical experiments have been conducted on real demand measurements across 2639 households in London, collected from Low Carbon London project's smart-metering trial. The mean absolute percentage error and the pinball loss function are used to quantitatively demonstrate the superiority of the proposed approach in terms of the point estimate value and the probabilistic result, respectively.