While environmental, social, and governance (ESG) trading activity has been a distinctive feature of financial markets, the debate if ESG scores can also convey information regarding a company's riskiness remains open. Regulatory authorities, such as the European Banking Authority (EBA), have acknowledged that ESG factors can contribute to risk. Therefore, it is important to model such risk dependencies and quantify what part of a company's riskiness can be attributed to the ESG scores. This paper aims to question whether ESG scores can be used to provide information on (tail) riskiness. By analyzing the (tail) dependence structure of companies with a range of ESG scores, that is within an ESG rating class, using high-dimensional vine copula modeling, we are able to show that risk can also depend on and be directly associated with a specific ESG rating class. Empirical findings on real-world data show positive not negligible ESG risks determined by ESG scores, especially during the 2008 crisis.

High-dimensional data sets are often available in genome-enabled predictions. Such data sets include nonlinear relationships with complex dependence structures. For such situations, vine copula-based (quantile) regression is an important tool. However, the current vine copula-based regression approaches do not scale up to high and ultra-high dimensions. To perform high-dimensional sparse vine copula-based regression, we propose 2 methods. First, we show their superiority regarding computational complexity over the existing methods. Second, we define relevant, irrelevant, and redundant explanatory variables for quantile regression. Then, we show our method's power in selecting relevant variables and prediction accuracy in high-dimensional sparse data sets via simulation studies. Next, we apply the proposed methods to the high-dimensional real data, aiming at the genomic prediction of maize traits. Some data processing and feature extraction steps for the real data are further discussed. Finally, we show the advantage of our methods over linear models and quantile regression forests in simulation studies and real data applications.

With the availability of massive multivariate data comes a need to develop flexible multivariate distribution classes. The copula approach allows marginal models to be constructed for each variable separately and joined with a dependence structure characterized by a copula. The class of multivariate copulas was limited for a long time to elliptical (including the Gaussian and t-copula) and Archimedean families (such as Clayton and Gumbel copulas). Both classes are rather restrictive with regard to symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by building a multivariate model using only bivariate building blocks. This gives rise to highly flexible models that still allow for computationally tractable estimation and model selection procedures. These features made vine copula models quite popular among applied researchers in numerous areas of science. This article reviews the basic ideas underlying these models, presents estimation and model selection approaches, and discusses current developments and future directions.

Climate change and sustainability have become societal focal points in the last decade. Consequently, companies have been increasingly characterized by non-financial information, such as environmental, social, and governance (ESG) scores, based on which companies can be grouped into ESG classes. While many scholars have questioned the relationship between financial performance and risks of assets belonging to different ESG classes, the question about dependence among ESG classes is still open. Here, we focus on understanding the dependence structures of different ESG class indices and the market index through the lens of copula models. After a thorough introduction to vine copula models, we explain how cross-sectional and temporal dependencies can be captured by models based on vine copulas, more specifically, using ARMA-GARCH and stationary vine copula models. Using real-world ESG data over a long period with different economic states, we find that assets with medium ESG scores tend to show weaker dependence to the market, while assets with extremely high or low ESG scores tend to show stronger, non-Gaussian dependence.

The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these dependencies, a novel vine copula mixture model for continuous data is proposed. The model selection and parameter estimation problems are discussed, and further, a new model-based clustering algorithm is formulated. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. The simulation experiments illustrate a significant gain in clustering accuracy when notably asymmetric tail dependencies or/and non-Gaussian margins within the components exist. The analysis of real data sets accompanies the proposed method. The model-based clustering algorithm with vine copula mixture models outperforms others, especially for the non-Gaussian multivariate data.

Evaluating companies' sustainability performance embraces environmental, social, and governance (ESG) activities. Data providers assign companies ESG scores as a quantitative measure based on available information. Refinitiv (previously ASSET4) is a key data provider whose scores are used extensively by researchers and companies; however, their ESG scoring methodology allows the scores from the five most recent years to change post-publication without any announcements. Such ESG scores are called non-definitive. Then, ESG research findings and companies' sustainability performance using the ESG data from the same data provider might be inconsistent. Optimization and exploratory data mining approaches show that it is possible to change ESG scores to exhibit stronger risk dependence. We discuss how the initial disclosure of ESG information and updating the published ESG information alter the way ESG scores are computed in a given industry group, impacting ESG research findings significantly. Moreover, the initial disclosure of ESG information and an update in the published ESG information might allow some companies to appear more sustainable, even though nothing has changed. Finally, our work indicates the criticality that should be addressed to improve comparability within research studies and companies' sustainability performance relying on data from the same ESG providers.

Environmental, Social, and Governance (ESG) scores measure companies' performance concerning sustainability and are organized in three pillars: Environmental, Social, and Governance. These complementary non-financial ESG scores should provide information about companies' ESG performance and risks. However, the extent of not yet published ESG information makes the reliability of ESG scores questionable. To explicitly capture the not yet published information on ESG category scores, a new pillar, the so-called Missing (M) pillar, is proposed and added to the new definition of the Environmental, Social, Governance, and Missing (ESGM) scores. By relying on the data provided by Refinitiv, we show that the ESGM scores strengthen the companies' risk relationship. These new scores could benefit investors and practitioners as ESG exclusion strategies using only ESG scores might exclude assets with a low score solely because of their missing information and not necessarily because of a low ESG merit.