Showing papers on "Vine copula published in 2018"

Probabilistic Forecast for Multiple Wind Farms Based on Regular Vine Copulas

Abstract: The uncertain nature of wind power causes difficulties in power system operation scheduling. Probabilistic descriptions of the uncertainty have been studied for decades. However, probabilistic forecasts designed for the regional multiple wind farms are few. Although the traditional methods for the single wind farm can still be used, they have the limitations in capturing the spatial correlations among wind farms, and they are less robust when multivariate observations are not so complete. To improve the forecast quality in this case, we combine the multivariate distribution modeling and probabilistic forecasts in this paper. An advanced model—the regular vine copula, which can describe the wind farms’ dependence structure precisely and flexibly with various bivariate copulas as blocks, is used in this paper. Enough simulation data can be generated from the model, which can be easily used to form the conditional forecast distributions under multiple forecast conditions. A case of 10 wind farms in East China has been used to compare the proposed method with its competitors. The results showed the method's advantages of providing reliable and sharp forecast intervals, especially in the case with limited observations available.

Copula approaches for modeling cross-sectional dependence of data breach losses

Abstract: Many experts claim that cyber risks are correlated, but there is not much supporting empirical evidence We consider 3,327 data breach events from 2005 to 2016 and identify a significant asymmetric dependence of monthly losses in two cross-sectional settings: cross-industry losses in four categories by breach types (hacking, lost electronic device, unintended disclosure and insider breach) and cross-breach type losses in five categories by industries (banking and insurance, government, medical service, retail/other business and educational institution) To identify the method that best fits the dependence structure of the dataset, we implement copula modeling by separating the dependence into pairwise non-zero losses and zero loss arrivals We model the former by pair copula construction (PCC) allowing for the flexible choice of copula functions, whereas the latter is modeled by Gaussian copula We illustrate the usefulness of our results in two applications to risk measurement and pricing Our findings are important for risk managers and actuaries who are designing cyber-insurance policies

A Framework for Exploring Joint Effects of Conditional Factors on Compound Floods

Abstract: This study highlights the features of vine copula for examining compound events involving underlying conditions that amply the compounding effects. To illustrate, we study compound floods in Texas (TX), USA. These compound floods consist of combinations of precipitation and surface runoff with the El Ni~ no-Southern Oscillation (ENSO) and rising temperatures as underlying conditions. Although the individual variable of precipitation and runoff may not itself be extreme, large exceedances can lead to flooding situations when combined. The presence of underlying conditions (e.g., El Ni~ no and/or rising temperatures) can exacerbate the associated flood impacts. We use observational data during May–August for each climate division of TX. A three-dimensional vine copula is used first to quantify the ENSO effect on precipitation and runoff through conditioning sets of vine copula. We further examine the interplay of a warming signal and El Ni~ no to reveal their mutual effects on compound floods by placing these two factors as interrelated conditions in a four-dimensional vine copula. Our results show that El Ni~ no is much stronger than the other ENSO states in conditioning a high likelihood of TX compound floods by amplifying mean and extreme states of rainfall and runoff. Conditioned by both El Ni~ no and global temperatures, a slight reduction occurs in TX compound floods under the warmer condition. This is consistent with the trend of precipitation and runoff composites under given conditions, while no appreciable changes are found to suggest a different joint effect of El Ni~ no and rising temperatures on TX compound floods.

The shifting dependence dynamics between the G7 stock markets

Abstract: The growing interdependence between financial markets has attracted special attention from academic researchers and finance practitioners for the purpose of optimal portfolio design and contagion analysis. This article develops a tractable regime-switching version of the copula functions to model the intermarkets linkages during turmoil and normal periods, while taking into account structural changes. More precisely, Markov regime-switching C-vine and D-vine decompositions of the Student’s t copula are proposed and applied to returns on diversified portfolios of stocks, represented by the G7 stock market indices. The empirical results show evidence of regime shifts in the dependence structure with high contagion risk during crisis periods. Moreover, both the C- and D-vines highly outperform the multivariate Student’s t copula, which suggests that the shock transmission path is as important as the dependence itself, and is better detected with a vine copula decomposition.

Standardized drought indices: a novel univariate and multivariate approach

Abstract: As drought is among the natural hazards which affects people and economies worldwide and often results in huge monetary losses sophisticated methods for drought monitoring and decision making are needed. Several different approaches to quantify drought have been developed during past decades. However, most of these drought indices suffer from different shortcomings and do not account for the multiple driving factors which promote drought conditions and their inter-dependencies. We provide a novel methodology for the calculation of (multivariate) drought indices, which combines the advantages of existing approaches and omits their disadvantages. Moreover, our approach benefits from the flexibility of vine copulas in modeling multivariate non-Gaussian inter-variable dependence structures. A three-variate data example is used in order to investigate drought conditions in Europe and to illustrate and reason the different modeling steps. The data analysis shows the appropriateness of the described methodology. Comparison to well-established drought indices shows the benefits of our multivariate approach. The validity of the new methodology is verified by comparing the spatial extent of historic drought events based on different drought indices. Further, we show that the assumption of non-Gaussian dependence structures is well-grounded in this real-world application.

Measuring Value-at-Risk and Expected Shortfall of crude oil portfolio using extreme value theory and vine copula

Abstract: Volatilities of crude oil price have important impacts on the steady and sustainable development of world real economy. Thus it is of great academic and practical significance to model and measure the volatility and risk of crude oil markets accurately. This paper aims to measure the Value-at-Risk (VaR) and Expected Shortfall (ES) of a portfolio consists of four crude oil assets by using GARCH-type models, extreme value theory (EVT) and vine copulas. The backtesting results show that the combination of GARCH-type-EVT models and vine copula methods can produce accurate risk measures of the oil portfolio. Mixed R-vine copula is more flexible and superior to other vine copulas. Different GARCH-type models, which can depict the long-memory and/or leverage effect of oil price volatilities, however offer similar marginal distributions of the oil returns.

Statistical arbitrage with vine copulas

Abstract: We develop a multivariate statistical arbitrage strategy based on vine copulas—a highly flexible instrument for linear and nonlinear multivariate dependence modeling. In an empirical application on...

PAR( p )-vine copula based model for stochastic streamflow scenario generation

Abstract: Synthetic streamflow data is vital for the energy sector, as it feeds stochastic optimisation models that determine operational policies. Considered scenarios should differ from each other, but be the same from a statistical point of view, i.e., the scenarios must preserve features of the original time series such as the mean, variance, and temporal dependence structures. Traditionally, linear models are applied for this task. Recently, the advent of copulas has led to the emergence of an alternative that overcomes the drawbacks of linear models. In this context, we propose a methodology based on vine copulas for the stochastic simulation of periodic streamflow scenarios. Copula-based models that focus on single-site inflow simulation only consider lag-one time dependence. Therefore, we suggest an approach that incorporates lags that are greater than one. Furthermore, the proposed model deals with the strong periodicity that is commonly present in monthly streamflow time series. The resulting model is a non-linear periodic autoregressive model. Our results indicate that this model successfully simulates scenarios, preserving features that are observed in historical data.

Estimating non-simplified vine copulas using penalized splines

Abstract: Vine copulas (or pair-copula constructions) have become an important tool for high-dimensional dependence modeling. Typically, so-called simplified vine copula models are estimated where bivariate conditional copulas are approximated by bivariate unconditional copulas. We present the first nonparametric estimator of a non-simplified vine copula that allows for varying conditional copulas using penalized hierarchical B-splines. Throughout the vine copula, we test for the simplifying assumption in each edge, establishing a data-driven non-simplified vine copula estimator. To overcome the curse of dimensionality, we approximate conditional copulas with more than one conditioning argument by a conditional copula with the first principal component as conditioning argument. An extensive simulation study is conducted, showing a substantial improvement in the out-of-sample Kullback–Leibler divergence if the null hypothesis of a simplified vine copula can be rejected. We apply our method to the famous uranium data and present a classification of an eye state data set, demonstrating the potential benefit that can be achieved when conditional copulas are modeled.

Stochastic Simulation of Test Collections: Evaluation Scores

Abstract: Part of Information Retrieval evaluation research is limited by the fact that we do not know the distributions of system effectiveness over the populations of topics and, by extension, their true mean scores. The workaround usually consists in resampling topics from an existing collection and approximating the statistics of interest with the observations made between random subsamples, as if one represented the population and the other a random sample. However, this methodology is clearly limited by the availability of data, the impossibility to control the properties of these data, and the fact that we do not really measure what we intend to. To overcome these limitations, we propose a method based on vine copulas for stochastic simulation of evaluation results where the true system distributions are known upfront. In the basic use case, it takes the scores from an existing collection to build a semi-parametric model representing the set of systems and the population of topics, which can then be used to make realistic simulations of the scores by the same systems but on random new topics. Our ability to simulate this kind of data not only eliminates the current limitations, but also offers new opportunities for research. As an example, we show the benefits of this approach in two sample applications replicating typical experiments found in the literature. We provide a full R package to simulate new data following the proposed method, which can also be used to fully reproduce the results in this paper.

Numerical comparison of multivariate models to forecasting risk measures

Abstract: We evaluated the performance of multivariate models for forecasting Value at Risk (VaR), Expected Shortfall (ES), and Expectile Value at Risk (EvaR). We used Historical Simulation (HS), Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedastic (DCC-GARCH) and copula methods: Regular copulas, Vine copulas, and Nested Archimedean copulas (NAC). We assessed the performance of the models using Monte Carlo simulations, considering different scenarios, regarding the marginal distributions, correlation, and number of portfolio assets. Numerical results evidenced the accuracy forecasting risk measures are associated with marginal distributions. For a data-generating process where the marginal distribution is Gaussian, Regular and Vine copulas demonstrated better performance. For data generated with Student’s t distribution, we verified better performance by NAC. In addition, we identified the superiority of copula methods over HS and DCC-GARCH, which reduces the model risk.

Nonlinear and Non-Gaussian Process Monitoring Based on Simplified R-Vine Copula

Abstract: In the field of chemical process monitoring, the vine copula model provides a new idea for describing the interdependence between high-dimensional complex variables, and directly characterizes the correlation without dimensional reduction. However, in actual industrial processes, the number of pair copulas to be optimized and the parameters to be estimated increase rapidly when the dimensionality of the variables is large. This greatly increases the computational load and reduces the detection efficiency. In this paper, a fault diagnosis method based on a simplified R-vine (SRV) model is proposed. Without reducing the precision of the model significantly, the simplified level is set to reduce the complexity of the workload and calculations. The simplified level of an R-vine model is obtained by a Vuong test. Then, the generalized local probability (GLP) of the non-Gaussian state is constructed by using the theory of highest density region (HDR) and a density quantile table. The monitoring results of the T...

Multivariate Modeling of Annual Instantaneous Maximum Flows Using Copulas

Abstract: Although copula functions have been successively applied to flood frequency analysis, their application has usually been restricted to modeling bivariate dependence. This is because higher-...

Vine copulas: modelling systemic risk and enhancing higher‐moment portfolio optimisation

Abstract: Asymmetric dependence in equities markets has been shown to have detrimental effects on portfolio diversification as assets within the portfolio exhibit greater correlations during market downturns compared to market upturns. By applying the Clayton canonical vine copula (CVC) to model asymmetric dependence, we produce a measure of systemic risk across a portfolio of assets. In addition, we use the Clayton CVC to produce estimates of expected returns in an application to higher-moment portfolio optimisation and find evidence of an improvement in performance across a range of risk-adjusted return measures and the indices of acceptability.

Copula-based agricultural conditional value-at-risk modelling for geographical diversifications in wheat farming portfolio management

Abstract: An agricultural producer's crop yield and the subsequent farming revenues are affected by many complex factors, including price fluctuations, government policy and climate (e.g., rainfall and temperature) extremes. Geographical diversification is identified as a potential farmer adaptation and decision support tool that could assist producers to reduce unfavourable financial impacts due to the variabilities in crop price and yield, associated with climate variations. There has been limited research performed on the effectiveness of this strategy. This paper proposes a new statistical approach to investigate whether the geographical spread of wheat farm portfolios across three climate broad-acre (i.e., rain-fed) zones could potentially reduce financial risks for producers in the Australian agro-ecological zones. A suite of popular and statistically robust tools applied in the financial sector based on the well-established statistical theories, comprised of the Conditional Value-at-Risk (CVaR) and the joint copula models were employed to evaluate the effectiveness geographical diversification. CVaR is utilised to benchmark the losses (i.e., the downside risk), while the copula function is employed to model the joint distribution among marginal returns (i.e., profit in each zone). The mean-CVaR optimisations indicate that geographical diversification could be a feasible agricultural risk management approach for wheat farm portfolio managers in achieving their optimised expected returns while controlling the risks (i.e., target levels of risk). Further, in this study, the copula-based mean-CVaR model is seen to better simulate extreme losses compared to the conventional multivariate-normal models, which underestimate the minimum risk levels at a given target of expected return. Among the suite of tested copula-based models, the vine copula in this study is found to be a superior in capturing the tail dependencies compared to the other multivariate copula models investigated. The present study provides innovative solutions to agricultural risk management with advanced statistical models using Australia as a case study region, also with broader implications to other regions where farming revenues may be optimized through copula-statistical models.

Financial stress relationships among Euro area countries: An R-vine Copula approach

Abstract: One of the biggest challenges of keeping Euro area financial stability is the negative co-movement between the vulnerability of public finance, the financial sector, security markets stresses as well as economic growth, especially in peripheral economies. This paper utilizes a ARMA-GARCH based R-vine copula method to explore tail dependance between the Financial Stress Indices of 11 euro area countries with an aim of understanding how financial stress are interacting with each other. We find larger economies in the Euro area tend to have closer upper tail dependence in terms of positive shocks, while smaller economies tend to have closer lower tail dependence with respect to negative shocks. The R-vine copula results underline the complex dynamics of financial stress relations existing between Euro Area economies. The estimated R-vine shows Spain, Italy, France and Belgium are the most inter-connected nodes which underlying they might be more efficient targets to treat in order to achieve a quicker stabilizing. Our results relate to the fact that Eurozone is not a unified policy making area, therefore, it needs to follow divergent policies for taming the effects of financial instability to different regions or groups of economies that are more interconnected.

Model distances for vine copulas in high dimensions

Abstract: Vine copulas are a flexible class of dependence models consisting of bivariate building blocks and have proven to be particularly useful in high dimensions. Classical model distance measures require multivariate integration and thus suffer from the curse of dimensionality. In this paper, we provide numerically tractable methods to measure the distance between two vine copulas even in high dimensions. For this purpose, we consecutively develop three new distance measures based on the Kullback–Leibler distance, using the result that it can be expressed as the sum over expectations of KL distances between univariate conditional densities, which can be easily obtained for vine copulas. To reduce numerical calculations, we approximate these expectations on adequately designed grids, outperforming Monte Carlo integration with respect to computational time. For the sake of interpretability, we provide a baseline calibration for the proposed distance measures. We further develop similar substitutes for the Jeffreys distance, a symmetrized version of the Kullback–Leibler distance. In numerous examples and applications, we illustrate the strengths and weaknesses of the developed distance measures.

Representing Sparse Gaussian DAGs as Sparse R-Vines Allowing for Non-Gaussian Dependence

Abstract: Modeling dependence in high-dimensional systems has become an increasingly important topic. Most approaches rely on the assumption of a multivariate Gaussian distribution such as statistical models on directed acyclic graphs (DAGs). They are based on modeling conditional independencies and are scalable to high dimensions. In contrast, vine copula models accommodate more elaborate features like tail dependence and asymmetry, as well as independent modeling of the marginals. This flexibility comes however at the cost of exponentially increasing complexity for model selection and estimation. We show a novel connection between DAGs with limited number of parents and truncated vine copulas under sufficient conditions. This motivates a more general procedure exploiting the fast model selection and estimation of sparse DAGs while allowing for non-Gaussian dependence using vine copulas. By numerical examples in hundreds of dimensions, we demonstrate that our approach outperforms the standard method for vi...

Learning Vine Copula Models For Synthetic Data Generation

Abstract: A vine copula model is a flexible high-dimensional dependence model which uses only bivariate building blocks. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. In this work, we formulate a vine structure learning problem with both vector and reinforcement learning representation. We use neural network to find the embeddings for the best possible vine model and generate a structure. Throughout experiments on synthetic and real-world datasets, we show that our proposed approach fits the data better in terms of log-likelihood. Moreover, we demonstrate that the model is able to generate high-quality samples in a variety of applications, making it a good candidate for synthetic data generation.

Enhancing Quality of Multivariate Process Monitoring Based on Vine Copula and Active Learning Strategy

Abstract: This paper proposes a new process monitoring method based on vine copula and active learning strategy under a limited number of labeled samples. The proposed method uses active learning strategy and the generalized Bayesian inference-based probability (GBIP) index to choose samples that can provide the most significant information for the process monitoring model. An adaptive strategy is used to select the number of training samples in every active learning loop. Then, the vine copula-based dependence description (VCDD) is used to fulfill fault detection for complex chemical processes. The validity and effectiveness of the proposed approach are illustrated using a numerical example and the Tennessee Eastman (TE) benchmark process. The results show that the proposed method can maximize the process monitoring performance while minimizing the number of samples labeled.

AD‐vine copula‐based model for repeated measurements extending linear mixed models with homogeneous correlation structure

Abstract: We propose a model for unbalanced longitudinal data, where the univariate margins can be selected arbitrarily and the dependence structure is described with the help of a D‐vine copula. We show that our approach is an extremely flexible extension of the widely used linear mixed model if the correlation is homogeneous over the considered individuals. As an alternative to joint maximum–likelihood a sequential estimation approach for the D‐vine copula is provided and validated in a simulation study. The model can handle missing values without being forced to discard data. Since conditional distributions are known analytically, we easily make predictions for future events. For model selection, we adjust the Bayesian information criterion to our situation. In an application to heart surgery data our model performs clearly better than competing linear mixed models.

Spatio-temporal synthesis of continuous precipitation series using vine copulas

Abstract: Long and continuous series of precipitation in a high temporal resolution are required for several purposes, namely, urban hydrological applications, design of flash flood control structures, etc. As data of the temporally required resolution is often available for short period, it is advantageous to develop a precipitation model to allow for the generation of long synthetic series. A stochastic model is applied for this purpose, involving an alternating renewal process (ARP) describing a system consisting of spells that can take two possible states: wet or dry. Stochastic generation of rainfall time series using ARP models is straight forward for single site simulation. The aim of this work is to present an extension of the model to spatio-temporal simulations. The proposed methodology combines an occurrence model to define in which locations rainfall events occur simultaneously with a multivariate copula to generate synthetic events. Rainfall series registered in different regions of Germany are used to develop and test the methodology. Results are compared with an existing method in which long independent time series of rainfall events are transformed to spatially dependent ones by permutation of their order. The proposed model shows to perform as a satisfactory extension of the ARP model for multiple sites simulations.

A Multivariate Volatility Vine Copula Model

Abstract: This article proposes a dynamic framework for modeling and forecasting of realized covariance matrices using vine copulas to allow for more flexible dependencies between assets. Our model automatically guarantees positive definiteness of the forecast through the use of a Cholesky decomposition of the realized covariance matrix. We explicitly account for long-memory behavior by using fractionally integrated autoregressive moving average (ARFIMA) and heterogeneous autoregressive (HAR) models for the individual elements of the decomposition. Furthermore, our model incorporates non-Gaussian innovations and GARCH effects, accounting for volatility clustering and unconditional kurtosis. The dependence structure between assets is studied using vine copula constructions, which allow for nonlinearity and asymmetry without suffering from an inflexible tail behavior or symmetry restrictions as in conventional multivariate models. Further, the copulas have a direct impact on the point forecasts of the realize...

Portfolio Diversification Strategy Via Tail‐Dependence Clustering and ARMA‐GARCH Vine Copula Approach

Abstract: This study proposes a diversified portfolio construction method based on the tail dependence between the financial assets and adopting both market prior information and the exports’ subject views In this paper, tail‐dependence clustering was applied to divide candidate assets into different groups according to their tail dependence during the crisis period and the ARMA‐GARCH vine copula‐opinion pooling approach was applied to select the minimum Conditional Value‐at‐Risk portfolio according to the clustering results The daily closed prices of the components of DAX 20 from 3 January 2006 to 20 December 2014 were studied to illustrate the methodology The results reveal that more than 90% of 450 possible portfolios are modelled by D‐vine structure and Student's t‐copula dominates almost all the cases for pair copula selection As Student's t‐copula captures the symmetric tail dependence, the 450 possible portfolios do not show stronger lower tail dependence than upper tail dependence This study contributes by combining cluster analysis with portfolios selection It uses vine copula to capture the dependence structure among assets Finally, it offers a flexible method to describe market and offers a strategy to construct diversified portfolios by adding the investors’ information into portfolio selection procedure at the 1‐day forecast horizon

Vine copula approximation : a generic method for coping with conditional dependence

Abstract: Pair-copula constructions (or vine copulas) are structured, in the layout of vines, with bivariate copulas and conditional bivariate copulas. The main contribution of the current work is an approach to the long-standing problem: how to cope with the dependence structure between the two conditioned variables indicated by an edge, acknowledging that the dependence structure changes with the values of the conditioning variables. The changeable dependence problem, though recognized as crucial in the field of multivariate modelling, remains widely unexplored due to its inherent complication and hence is the motivation of the current work. Rather than resorting to traditional parametric or nonparametric methods, we proceed from an innovative viewpoint: approximating a conditional copula, to any required degree of approximation, by utilizing a family of basis functions. We fully incorporate the impact of the conditioning variables on the functional form of a conditional copula by employing local learning methods. The attractions and dilemmas of the pair-copula approximating technique are revealed via simulated data, and its practical importance is evidenced via a real data set.

Conditional dependence between oil price and stock prices of renewable energy: a vine copula approach

Abstract: The current paper focusses on the co-movement between oil prices and renewable energy stock markets in a multivariate framework. The vine copula approach that offers a great flexibility in conditio...

Nonparametric Forecasting of Multivariate Probability Density Functions

Abstract: The study of dependence between random variables is the core of theoretical and applied statistics. Static and dynamic copula models are useful for describing the dependence structure, which is fully encrypted in the copula probability density function. However, these models are not always able to describe the temporal change of the dependence patterns, which is a key characteristic of financial data. We propose a novel nonparametric framework for modelling a time series of copula probability density functions, which allows to forecast the entire function without the need of post-processing procedures to grant positiveness and unit integral. We exploit a suitable isometry that allows to transfer the analysis in a subset of the space of square integrable functions, where we build on nonparametric functional data analysis techniques to perform the analysis. The framework does not assume the densities to belong to any parametric family and it can be successfully applied also to general multivariate probability density functions with bounded or unbounded support. Finally, a noteworthy field of application pertains the study of time varying networks represented through vine copula models. We apply the proposed methodology for estimating and forecasting the time varying dependence structure between the S&P500 and NASDAQ indices.