Showing papers on "Vine copula published in 2014"

Dependence Modeling with Copulas

Abstract: Introduction Dependence modeling Early research for multivariate non-Gaussian Copula representation for a multivariate distribution Data examples: scatterplots and semi-correlations Likelihood analysis and model comparisons Copula models versus alternative multivariate models Terminology for multivariate distributions with U(0, 1) margins Copula constructions and properties Basics: Dependence, Tail Behavior, and Asymmetries Multivariate cdfs and their conditional distributions Laplace transforms Extreme value theory Tail heaviness Probability integral transform Multivariate Gaussian/normal Elliptical and multivariate t distributions Multivariate dependence concepts Frechet classes and Frechet bounds, given univariate margins Frechet classes given higher order margins Concordance and other dependence orderings Measures of bivariate monotone association Tail dependence Tail asymmetry Measures of bivariate asymmetry Tail order Semi-correlations of normal scores for a bivariate copula Tail dependence functions Strength of dependence in tails and boundary conditional cdfs Conditional tail expectation for bivariate distributions Tail comonotonicity Summary for analysis of properties of copulas Copula Construction Methods Overview of dependence structures and desirable properties Archimedean copulas based on frailty/resilience Archimedean copulas based on Williamson transform Hierarchical Archimedean and dependence Mixtures of max-id Another limit for max-id distributions Frechet class given bivariate margins Mixtures of conditional distributions Vine copulas or pair-copula constructions Factor copula models Combining models for different groups of variables Nonlinear structural equation models Truncated vines, factor models and graphical models Copulas for stationary time series models Multivariate extreme value distributions Multivariate extreme value distributions with factor structure Other multivariate models Operations to get additional copulas Summary for construction methods Parametric Copula Families and Properties Summary of parametric copula families Properties of classes of bivariate copulas Gaussian Plackett Copulas based on the logarithmic series LT Copulas based on the gamma LT Copulas based on the Sibuya LT Copulas based on the positive stable LT Galambos extreme value Husler-Reiss extreme value Archimedean with LT that is integral of positive stable Archimedean based on LT of inverse gamma Multivariate tv Marshall-Olkin multivariate exponential Asymmetric Gumbel/Galambos copulas Extreme value limit of multivariate tv Copulas based on the gamma stopped positive stable LT Copulas based on the gamma stopped gamma LT Copulas based on the positive stable stopped gamma LT Gamma power mixture of Galambos Positive stable power mixture of Galambos Copulas based on the Sibuya stopped positive stable LT Copulas based on the Sibuya stopped gamma LT Copulas based on the LT of generalized Sibuya Copulas based on the tilted positive stable LT Copulas based on the shifted negative binomial LT Multivariate GB2 distribution and copula Factor models based on convolution-closed families Morgenstern or FGM Frechet's convex combination Additional parametric copula families Dependence comparisons Summary for parametric copula families Inference, Diagnostics, and Model Selection Parametric inference for copulas Likelihood inference Log-likelihood for copula models Maximum likelihood: asymptotic theory Inference functions and estimating equations Composite likelihood Kullback-Leibler divergence Initial data analysis for copula models Copula pseudo likelihood, sensitivity analysis Non-parametric inference Diagnostics for conditional dependence Diagnostics for adequacy of fit Vuong's procedure for parametric model comparisons Summary for inference Computing and Algorithms Roots of nonlinear equations Numerical optimization and maximum likelihood Numerical integration and quadrature Interpolation Numerical methods involving matrices Graphs and spanning trees Computation of tau, rhoS, and rhoN for copulas Computation of empirical Kendall's tau Simulation from multivariate distributions and copulas Likelihood for vine copula Likelihood for factor copula Copula derivatives for factor and vine copulas Generation of vines Simulation from vines and truncated vine models Partial correlations and vines Partial correlations and factor structure Searching for good truncated R-vine approximations Summary for algorithms Applications and Data Examples Data analysis with misspecified copula models Inferences on tail quantities Discretized multivariate Gaussian and R-vine approximation Insurance losses: bivariate continuous Longitudinal count: multivariate discrete Count time series Multivariate extreme values Multivariate financial returns Conservative tail inference Item response: multivariate ordinal SEM model as vine: alienation data SEM model as vine: attitude-behavior data Overview of applications Theorems for Properties of Copulas Absolutely continuous and singular components of multivariate distributions Continuity properties of copulas Dependence concepts Frechet classes and compatibility Archimedean copulas Multivariate extreme value distributions Mixtures of max-id distributions Elliptical distributions Tail dependence Tail order Combinatorics of vines Vines and mixtures of conditional distributions Factor copulas Kendall functions Laplace transforms Regular variation Summary for further research Appendix: Laplace Transforms and Archimedean Generators Index

Modelling skewed spatial random fields through the spatial vine copula

Abstract: a b s t r a c t Studying phenomena that follow a skewed distribution and entail an extremal behaviour is important in many disciplines. How to describe and model the dependence of skewed spatial random fields is still a challenging question. Especially when one is interested in interpolating a sample from a spatial random field that exhibits extreme events, classical geostatistical tools like kriging relying on the Gaussian assumption fail in reproducing the extremes. Originating from the multivariate extreme value theory partly driven by financial mathematics, copulas emerged in recent years being capable of describing different kinds of joint tail behaviours beyond the Gaussian realm. In this paper spatial vine copulas are introduced that are parametrized by distance and allow to include extremal behaviour of a spatial random field. The newly introduced distributions are fitted to the widely studied emergency and routine scenario data set from the spatial interpolation comparison 2004 (SIC2004). The presented spatial vine copula ranks within the top 5 approaches and is superior to all approaches in terms of the mean absolute error.

Estimation of the distribution of annual runoff from climatic variables using copulas

Abstract: An approach of deriving the annual runoff distribution using copulas from an annual rainfall-runoff model is proposed to provide an alternative annual runoff frequency analysis method in case of changing climatic variables. The annual rainfall-runoff model is established on the basis of the Budyko formula to estimate annual runoff, with annual precipitation and potential evapotranspiration as input variables. The model contains one single parameter k that guarantees that annual water balance is satisfied. In the derivation of the annual runoff distribution, annual precipitation, annual potential evapotranspiration, and parameter k are treated as three random variables, while the annual runoff distribution is obtained by integrating the joint probability density function of the three random variables over the domain constrained by the annual rainfall-runoff model using the canonical vine copula. This copula-based derivation approach is tested for 40 watersheds in two large basins in China. The estimated annual runoff distribution performs well in most watersheds. The performance is mainly related to the accuracy of the marginal distribution of precipitation. The copula-based derivation approach can also be used in ungauged watersheds where the distribution of k at the local site is estimated from the regional information of the k variable, and it also has acceptable performance in most watersheds, while poor performance is observed in a few watersheds with low accuracy in the Budyko formula.

Forecasting VaR and ES of stock index portfolio: A Vine copula method

Abstract: Risk measurement has both theoretical and practical significance in risk management. Using daily sample of 10 international stock indices, firstly this paper models the internal structures among different stock markets with C-Vine, D-Vine and R-Vine copula models. Secondly, the Value-at-Risk (VaR) and Expected Shortfall (ES) of the international stock markets portfolio are forecasted using Monte Carlo method based on the estimated dependence of different Vine copulas. Finally, the accuracy of VaR and ES measurements obtained from different statistical models are evaluated by UC, IND, CC and Posterior analysis. The empirical results show that the VaR forecasts at the quantile levels of 0.9, 0.95, 0.975 and 0.99 with three kinds of Vine copula models are sufficiently accurate. Several traditional methods, such as historical simulation, mean-variance and DCC-GARCH models, fail to pass the CC backtesting. The Vine copula methods can accurately forecast the ES of the portfolio on the base of VaR measurement, and D-Vine copula model is superior to other Vine copulas.

R-vine Models for Spatial Time Series with an Application to Daily Mean Temperature

Abstract: We introduce an extension of R-vine copula models for the purpose of spatial dependency modeling and model based prediction at unobserved locations. The newly derived spatial R-vine model combines the flexibility of vine copulas with the classical geostatistical idea of modeling spatial dependencies by means of the distances between the variable locations. In particular the model is able to capture non-Gaussian spatial dependencies. For the purpose of model development and as an illustration we consider daily mean temperature data observed at 54 monitoring stations in Germany. We identify a relationship between the vine copula parameters and the station distances and exploit it in order to reduce the huge number of parameters needed to parametrize a 54-dimensional R-vine model needed to fit the data. The new distance based model parametrization results in a distinct reduction in the number of parameters and makes parameter estimation and prediction at unobserved locations feasible. The prediction capabilities are validated using adequate scoring techniques, showing a better performance of the spatial R-vine copula model compared to a Gaussian spatial model.

Some Comments on Copula-Based Regression

Abstract: In a recent article, Noh, El Ghouch, and Bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This comment investigates the effect which occurs under misspecification of the parametric model. We demonstrate by means of several examples that even for a one or two-dimensional predictor the error caused by a “wrong” specification of the parametric family is rather severe, if the regression is not monotone in one of the components of the predictor. Moreover, we also show that these problems occur for all of the commonly used copula families and we illustrate in several examples that the copula-based regression may lead to invalid results even when flexible copula models such as vine copulas (with the common parametric families) are used in the estimation procedure.

Spatial composite likelihood inference using local C-vines

Abstract: We present a vine copula based composite likelihood approach to model spatial dependencies, which allows to perform prediction at arbitrary locations. This approach combines established methods to model (spatial) dependencies. On the one hand the geostatistical concept utilizing spatial differences between the variable locations to model the extend of spatial dependencies is applied. On the other hand the flexible class of C-vine copulas is utilized to model the spatial dependency structure locally. These local C-vine copulas are parametrized jointly, exploiting an existing relationship between the copula parameters and the respective spatial distances and elevation differences, and are combined in a composite likelihood approach. The new methodology called spatial local C-vine composite likelihood (S-LCVCL) method benefits from the fact that it is able to capture non-Gaussian dependency structures. The development and validation of the new methodology is illustrated using a data set of daily mean temperatures observed at 73 observation stations spread over Germany. For validation continuous ranked probability scores are utilized. Comparison with two other approaches of spatial dependency modeling introduced in yet unpublished work of Erhardt, Czado and Schepsmeier (2014) shows a preference for the local C-vine composite likelihood approach.

Sequential Dependence Modeling Using Bayesian Theory and D-Vine Copula and Its Application on Chemical Process Risk Prediction

Abstract: An emerging kind of prediction model for sequential data with multiple time series is proposed. Because D-vine copula provides more flexibility in dependence modeling, accounting for conditional dependence, asymmetries, and tail dependence, it is employed to describe sequential dependence between variables in the sample data. A D-vine model with the form of a time window is created to fit the correlation of variables well. To describe the randomness dynamically, Bayesian theory is also applied. As an application, a detailed modeling of prediction of abnormal events in a chemical process is given. Statistics (e.g., mean, variance, skewness, kurtosis, confidence interval, etc.) of the posterior predictive distribution are obtained by Markov chain Monte Carlo simulation. It is shown that the model created in this paper achieves a prediction performance better than that of some other system identification methods, e.g., autoregressive moving average model and back propagation neural network.

A Vine Copula Approach for Analyzing Financial Risk and Co-movement of the Indonesian, Philippine and Thailand Stock Markets

Abstract: This paper aims at analyzing the financial risk and co-movement of stock markets in three countries: Indonesia, Philippine and Thailand. It consists of analyzing the conditional volatility and test the leverage effect in the stock markets of the three countries. To capture the pairwise and conditional dependence between the variables, we use the method of vine copulas. In addition, we illustrate the computations of the value at risk and the expected shortfall using Monte Carlo simulation with copula based GJR-GARCH model. The empirical evidence shows that all the leverage effects add much to the capacity for explanation of the three stock returns, and that the D-vine structure is more appropriate than the C-vine one for describing the dependence of the three stock markets. In addition, the value at risk and ES provide the evidence to confirm that the portfolio may avoid risk in significant measure.

Risk Analysis in Asian Emerging Markets using Canonical Vine Copula and Extreme Value Theory

Abstract: Normal distributions are appropriate to describe the behavior of stockmarket returns only when returns do not exhibit extreme behavior. This studyexamined extreme value theory (EVT) to capture more precisely the tail distri-bution of market risk with vine copula and to identify the dependence structuresbetween Asian emerging markets. We used value at risk (VaR) and conditionalvalue at risk (CVaR), based on simulation method, to measure the market riskand portfolio optimization. Our empirical ndings are that the conditional depen-dence between asymmetric volatility among ve markets are positive and have thedependence between Indian and Thai stronger than other markets. The results ofVaR and CVaR show that the Chinese market has the highest risk.

Vine Copula-Cross Entropy Evaluation of Dependence Structure and Financial Risk in Agricultural Commodity Index Returns

Abstract: Many studies used the empirical Kendall’s tau to select a preferable ordering of vine copulas or to fix such a sequence. In this study, for high dimension vine copulas, we propose the vine copula based cross entropy method to figure out a more appropriate ordering of the vine copula. The goal of this study is to estimate the non-conditional, conditional, and tail dependences for agricultural price index returns by using the C-vine and D-vine copula based cross entropy model. In addition, we show that a framework uses the Monte Carlo simulation and the results of vine copula to estimate the expected shortfall (ES) of an equally weighted portfolio. The optimal portfolio allocations can also be estimated using global optimization with the differential evolution algorithm.

Predicting the frequency of abnormal events in chemical process with Bayesian theory and vine copula

Abstract: Chemical accidents, such as an explosion, are of low frequency and high consequence (eg casualties, significant economic losses, pollution) Due to the shortage of accident data, recently, precursor data have received much attention in chemical risk analysis Usually, in chemical processes, an abnormal event can be seen as a precursor, which can propagate into near-miss, incident or even accident The abnormal event frequency (AEF) is defined as the number of abnormal events in a time interval, which can be an early indicator of risk In this paper, an AEF predicting model based on Bayesian theory and D-vine copula is proposed Generally, a chemical process is managed in shifts by several teams The AEFs vary with different experience and operational skills of the operator teams Furthermore, the previous operating team has an effect on the following operator teams and the effects are asymmetric between two teams, hence, D-vine copula is employed to describe the dependence with much flexibility Finally, the proposed method is applied to a case study of 4-group-3-shift, and the simulation result shows that it has a better performance compared to conventional approaches

Modeling Asymmetry and Tail Dependence among Multiple Variables by Using Partial Regular Vine.

Abstract: Modeling high-dimensional dependence is widely studied to explore deep relations in multiple variables particularly useful for financial risk assessment. Very often, strong restrictions are applied on a dependence structure by existing high-dimensional dependence models. These restrictions disabled the detection of sophisticated structures such as asymmetry, upper and lower tail dependence between multiple variables. The paper proposes a partial regular vine copula model to relax these restrictions. The new model employs partial correlation to construct the regular vine structure, which is algebraically independent. This model is also able to capture the asymmetric characteristics among multiple variables by using two-parametric copula with flexible lower and upper tail dependence. Our method is tested on a cross-country stock market data set to analyse the asymmetry and tail dependence. The high prediction performance is examined by the Value at Risk, which is a commonly adopted evaluation measure in financial market.

Studying Volatility and Dependency of Chinese Outbound Tourism Demand in Singapore, Malaysia, and Thailand: A Vine Copula Approach

Abstract: This paper investigates the volatility and dependence of Chinese tourism demand for Singapore, Malaysia, and Thailand (SMT) destinations, using the vine copula based auto regression moving average-generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. It is found that a jolt to the tourist flow can have long-standing ramifications for the SMT countries. The estimation of the vine copulas among SMT show that the Survival Gumbel, Frank, and Gaussian copulas are the best copulas for Canonical vine (C-vine) or Drawable vine (D-vine) among the possible pair-copulas. In addition, this paper illustrates the making of time-varying Frank copulas for vine copulas. Finally, there is a discussion on tourism policy planning for better managing the tourism demand for the SMT countries. We suggest tour operators and national tourism promotion authorities of SMT collaborate closely in the marketing and promotion of joint tourism products.

Estimating standard errors and efficient goodness-of-fit tests for regular vine copula models

Abstract: In this thesis we consider regular vine (R-vine) copula models, which are constructed hierarchically from only bivariate copulas. We introduce theory and algorithms for the computation of the score function and the observed information matrix in R-vine models enabling the estimation of parameter standard errors. We introduce two new goodness-of-fit tests arising from the information matrix test. The test statistics are derived and their asymptotic distribution proven. Further 13 tests are adapted from the bivariate case and compared in an extensive power study.

Dependence Analysis of Exchange Rate and International Trade of Thailand: Application of Vine Copulas

Abstract: This paper aims to investigate the correlation of multivariate dependences between the international trade of Thailand and the USD/THB exchange rate using vine copulas, including canonical (C-vine) and drawable (D-vine) vine copulas which are very flexible dependency structures.Another advantage is that thesemethods overcome limitations and complex dependencymodels. Before we built the paircopula constructions of the vine models, ARMA(1,1)-GARCH(1,1) was adopted to remove time dependence in each of the marginal time series. Furthermore, we got the various standardized residuals to transform into appropriate uniform margins [0,1]. The results can be seen for C-vine case, Gaussian, Rotated Joe, and BB1 which are suitable bivariate copula families for each pair-copula construction. On the other hand, D-vine case, Gaussian, and Rotated Joe are appropriate copula families for the pair-copula construction. In addition, the sequential log-likelihood is quite close to the one obtained by joint maximization; it means that both the vine models are appropriate-fit models. In order to confirm that it is not possible to distinguish between the two models, we employed the Vuong and Clarke tests to verify the suitability of the non-nested model. These tests confirm that the C-vine and Dvine copulas are not distinguishable. It can be concluded that our pair constructions of the time-varying Gaussian copula could be appropriate fits, better than those of the static copula. This study will help policy makers take action to combat the exchange rate volatility.

Vine Copulas as a Way to Describe and Analyze Multi-Variate Dependence in Econometrics: Computational Motivation and Comparison with Bayesian Networks and Fuzzy Approaches

Abstract: In the last decade, vine copulas emerged as a new efficient techniques for describing and analyzing multi-variate dependence in econometrics; see, e.g., [1, 2, 3, 7, 9, 10, 11, 13, 14, 21]. Our experience has shown, however, that while these techniques have been successfully applied to many practical problems of econometrics, there is still a lot of confusion and misunderstanding related to vine copulas. In this paper, we provide a motivation for this new technique from the computational viewpoint. We show that other techniques used to described dependence - Bayesian networks and fuzzy techniques - can be viewed as a particular case of vine copulas.

Measuring Systemic Risk: Copula CoVaR

Abstract: Although copula modeling has been applied in a growing number of financial applications, high-dimensional copula modeling is still in its early stages. Vine copula modeling not only has the advantage of extending to higher dimensions easily, but also provides a more flexible measure to capture an asymmetric dependence among assets. CoVaR, the Value-at-Risk of institutions conditional on other institutions being in distress, is introduced by Adrian and Brunnermeier (2011). ∆CoVaR is the risk contribution that the institution adds to the entire system. Combined with the modified CoVaR methodology and estimation of the dependence structures through vine copula modeling, we empirically investigate systemic risk in 10 S&P 500 sector indices in the U.S. stock market by estimating daily Copula ∆CoVaR and Copula ∆CoES from January 1, 1995 to July 31, 2013. Our model (Copula CoVaR) reveals a real-time and efficient tool that can be used to analyze systemic risk. Furthermore, this approach could offer a systemic risk index for those countries which do not have an instrument like VIX, and can be tailored to any underlying sector, country or financial market easily.

Modeling Dependency in Tourist Arrivals to Thailand from China, Korea, and Japan Using Vine Copulas

Abstract: Market interdependence has always been an interesting topic in the study of tourism demand. China, Japan, and Korea are important tourist markets for Thailand tourism. Understanding how the arrivals relate to each other can help in tourism management, in a way that it prepares the tourism industry to plan for the risk management of the tourism demand and tourism supply. The vine copula model was used to analyze the multiple dependencies by decomposing the diversity of the paircopulas which can be arranged and analyzed in a tree structure. For this study, both the C-vine copula and the D-vine copula were used to answer the research question. We give the same conditioning variable for both the C-vine and the D-vine copula models in order to find the answer to our question of whether these two models would give different results. The contributions of the study are obtained from the findings. The C-vine and D-vine copulas provided three pair-copulas, namely, China-Korea, China-Japan, and Korea-Japan given China and there exists a weak positive dependence in each pair. In addition, the results provide evidence that China has influence on the dependence between the tourist arrivals from Korea and Japan. Moreover, the three dimensions of the C-vine and D-vine copula models, which are given the same conditioning variable in the second tree, optimally provide the same estimates of the parameters of interest.

Copula-based high dimensional dependence modelling

Abstract: Big data applications increasingly involve high-dimensional and sophisticated dependence structures in complex data. Modelling high-dimensional dependence, that is, the dependence between a set of high-dimensional variables, is a critical but challenging issue in many applications including social media analysis and financial markets. A typical example concerns the interplay of financial variables involved in driving complex market movements. A particular problem is understanding the dependence between high-dimensional variables with tail dependence and asymmetric characteristics which appear widely in financial markets. Typically, existing methods, such as the Bayesian logic program, relational dependency networks and relational Markov networks, build a graph to represent the conditional dependence structure between random variables. These models aim at high-dimensional domains, and have the advantage of learning latent relationships from data. However, they tend to force the local quantitative part of the model to take a simple form such as the discretized form of the data when multivariate Gaussian or its mixtures cannot capture the data in the real world. The complex dependencies between high-dimensional variables are difficult to capture. In statistics and finance, the copula has been shown to be a powerful tool for modelling high-dimensional dependencies. The copula splits the multivariate marginal distributions from dependence structures, so that the specification of dependence structures can be investigated independently of the marginal distributions. It can provide a flexible mechanism for modelling real world distributions that cannot be handled well by graphical models. Thus, researchers have tried to combine copula and probability graphical models, such as the tree-structured copula model and copula Bayesian networks. These copula-based models aim to resolve the limitations of discretizing data, but they impose assumptions and restrictions on the dependence structure. These assumptions and restrictions are not appropriate for dependence modelling among financial variables. In order to address these research limitations and challenges, this thesis proposes the use of the truncated partial correlation-based canonical vine copula, partial correlation-based regular vine copula and truncated partial correlation-based regular vine copula to model the dependence of high-dimensional variables. Chapter 3 introduces a new partial correlation-based canonical vine to identify the asymmetric and non-linear dependence structures of asset returns without any prior dependence assumptions. To simplify the model while maintaining its merit, a partial correlation-based truncation method is proposed to truncate the canonical vine. The truncated partial correlation-based canonical vine copula is then applied to construct and analyse the dependence structures of European stocks as a case study. Chapter 4 introduces the truncated partial correlation-based regular vine copula to explore the relations in multiple variables.…

Risk Measurement and Risk Modelling Using Applications of Vine Copulas

Abstract: This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually applied to pairs of securities. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. The paper features the use of Regular Vine copulas in an analysis of the co-dependencies of 10 major European Stock Markets, as represented by individual market indices and the composite STOXX 50 index. The sample runs from 2005 to the end of 2011 to permit an exploration of how correlations change in different economic circumstances using three different sample periods: pre-GFC (Jan 2005- July 2007), GFC (July 2007-Sep 2009), and post-GFC periods (Sep 2009 - Dec 2011). The empirical results suggest that the dependencies change in a complex manner, and are subject to change in different economic circumstances. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co-dependencies. The practical application of Regular Vine metrics is demonstrated via an example of the calculation of the VaR of a portfolio made up of the indices.

Analysis of International Trade, Exchange Rate and Crude Oil Price on Economic Development of Yunnan Province: A GARCH-Vine Copula Model Approach

Abstract: In this paper, we attempted to use the GARCH-vine copula model toanalyze the dependence structure of international trade, exchange rate, and crudeoil price on the economic development of Yunnan Province. In the C-vine, thedf of the student-t copula model is signicant on C14 and C25j1, and there is theleast degree of freedom in C14, which means that there is a greater probabilityof extreme values in industrial added value and export. In the Clayton copula,we nd a strong signicance with fminunc in C13 and C45j123. With fminuncin C13, the Clayton copula can catch left tail dependence. This means that adecrease in the crude oil spot price is inclined to retard Yunnan's industrial addedvalue growth. In the D-vine, we nd that the df of the student-t copula modelvaries considerably and signicantly in C23 and C34, respectively. Finally, in theClayton copula, we conclude that there exists a strong signicance with fminuncin C45 (export-import) and C13j2.

A Mixture of Canonical Vine Copula-GARCH Approach for Modeling Dependence of European Electricity Markets

Abstract: This paper employed a mixed Canonical Vine Copula-GARCH ap-proach for modeling the dependence structures of European electricity markets.The electricity spot prices are taken from French, German, Spanish, Dutch, andBritish markets. The empirical result shows that pairwise positive dependencebetween markets is represented in Tree 1, in which there is positive spillover eectbetween the French and the other four markets. Moreover, the French, German,and Dutch markets have strong symmetric tail dependence, which suggests onemarket (one of the French, German, or Dutch markets) experiencing spikes ordrops, conditional on the event that the other two markets are also experiencingspikes or drops. Additionally, we also found that when adding the condition underone or more markets, the relationships of some pairs still had dependence, whilesome other pairs became independent.

An Analysis of Interdependencies among Energy, Biofuel, and Agricultural Markets Using Vine Copula Model

Abstract: This paper aims to study the structure of interdependencies between the energy, biofuel and agricultural commodity markets. The work concentrates on the dependence between ethanol and agricultural futures returns conditional to crude oil returns, and interdependence among agricultural commodities conditional to crude oil and ethanol futures returns. The C-vine copula based ARMA-GARCH model was used to explain the dependence structure of crude oil and the four related variables, and applied to investigate the risk of energy-agricultural commodity futures portfolio.We generally found symmetry in the tail dependence between the energy, biofuel, and agricultural commodities, and also found a greater significant variability in dependence, specifically, the dependence between the ethanol and agricultural commodity futures returns conditional to crude oil as well as interdependence between corn and soybean conditional to crude oil and ethanol return. This indicates that there is a rise in ethanol productions and that higher crude oil prices have caused a price increase in agricultural commodities such as corn and soybean. Moreover, the higher dynamic dependence and symmetric tail dependences indicate that opportunities for portfolio diversification are reduced, particularly during a downturn in the markets. Finally, our result suggests that the time-varying copula model captures the portfolio risk better than the static copula models.

Modelling of dependence in high-dimensional financial time series by cluster-derived canonical vines

Abstract: We extend existing models in the financial literature by introducing a cluster-derived canonical vine (CDCV) copula model for capturing high dimensional dependence between financial time series. This model utilises a simplified market-sector vine copula framework similar to those introduced by Heinen and Valdesogo (2008) and Brechmann and Czado (2013), which can be applied by conditioning asset time series on a market-sector hierarchy of indexes. While this has been shown by the aforementioned authors to control the excessive parameterisation of vine copulas in high dimensions, their models have relied on the provision of externally sourced market and sector indexes, limiting their wider applicability due to the imposition of restrictions on the number and composition of such sectors. By implementing the CDCV model, we demonstrate that such reliance on external indexes is redundant as we can achieve equivalent or improved performance by deriving a hierarchy of indexes directly from a clustering of the asset time series, thus abstracting the modelling process from the underlying data.