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In many time-to-event studies, the event of interest is recurrent. Here, the data for each sample unit correspond to a series of gap times between the subsequent events. Given a limited follow-up period, the last gap time might be right-censored. In contrast to classical analysis, gap times and censoring times cannot be assumed independent, i.e., the sequential nature of the data induces dependent censoring. Also, the number of recurrences typically varies among sample units leading to unbalanced data. To model the association pattern between gap times, so far only parametric margins combined with the restrictive class of Archimedean copulas have been considered. Here, taking the specific data features into account, we extend existing work in several directions: we allow for nonparametric margins and consider the flexible class of D-vine copulas. A global and sequential (one- and two-stage) likelihood approach are suggested. We discuss the computational efficiency of each estimation strategy. Extensive simulations show good finite sample performance of the proposed methodology. It is used to analyze the association of recurrent asthma attacks in children. The analysis reveals that a D-vine copula detects relevant insights, on how dependence changes in strength and type over time.

The intermittent and uncertain properties of wind power have presented enormous obstacles to the planning and steady operation of power systems. In this context, as an effective technique to study wind power uncertainty, the development of an accurate wind speed scenario generation method is of great significance for evaluating the impact of wind power in the power system. In the case of several wind farms, accurate scenario generation involves precise acquisition of the correlation between wind speeds and the greatest retention of statistical properties of wind speed data. Under this goal, this research provided a new method for scenario development based on principle component (PC) and R-vine copula theories that incorporates the spatiotemporal correlation of wind speeds. By integrating with PC theory, this strategy avoids the dimension disaster induced by employing R-vine copula alone while taking benefit of its flexibility. The simulation results utilizing the historical wind speeds of three adjacent wind farms as samples showed that the method described in this article could effectively preserve the statistical properties of wind speed data. Eight evaluation indicators covering three facets of the scenario generation method were used to compare the proposed method holistically to two other commonly used scenario generation methods. The results indicated that this method’s accuracy was increased further. Additionally, the validity and necessity of applying R-vine copula in this model was demonstrated through comparisons to C-vine and D-vine copulas.

A spatial quantile regression model is proposed to estimate the quantile curve for a given probability of non-exceedance, as function of locations and covariates. Canonical vines copulas are considered to represent the spatial dependence structure. The marginal at each location is an asymmetric Laplace distribution where the parameters are functions of the covariates. The full conditional quantile distribution is given using the Joe–Clayton copula. Simulations show the flexibility of the proposed model to estimate the quantiles with special dependence structures. A case study illustrates its applicability to estimate quantiles for spatial temperature anomalies.

Recently, the area of sea ice is rapidly decreasing due to global warming, and since the Arctic sea ice has a great impact on climate change, interest in this is increasing very much all over the world. In fact, the area of sea ice reached a record low in September 2012 after satellite observations began in late 1979. In addition, in early 2018, the glacier on the northern coast of Greenland began to collapse. If we are interested in record values of sea ice area, modeling relationships of these values and predicting future record values can be a very important issue because the record values that consist of larger or smaller values than the preceding observations are very closely related to each other. The relationship between the record values can be modeled based on the pivotal quantity and canonical and drawable vine copulas, and the relationship is called a dependence structure. In addition, predictions for future record values can be solved in a very concise way based on the pivotal quantity. To accomplish that, this article proposes an approach to model the dependence structure between record values based on the canonical and drawable vine. To do this, unknown parameters of a probability distribution need to be estimated first, and the pivotal-based method is provided. In the pivotal-based estimation, a new algorithm to deal with a nuisance parameter is proposed. This method allows one to reduce computational complexity when constructing exact confidence intervals of functions with unknown parameters. This method not only reduces computational complexity when constructing exact confidence intervals of functions with unknown parameters, but is also very useful for obtaining the replicated data needed to model the dependence structure based on canonical and drawable vine. In addition, prediction methods for future record values are proposed with the pivotal quantity, and we compared them with a time series forecasting method in real data analysis. The validity of the proposed methods was examined through Monte Carlo simulations and analysis for Arctic sea ice data.

We measured the systemic impact of financial distress in a Spanish listed bank on other listed banks and on the European financial system, using conditional value at risk (CoVaR) as a systemic risk measure. We modelled multivariate dependence between listed banks using a hierarchical tree structure given by a vine copula model and, using bivariate copulas, dependence between listed banks and the European financial system. For the period January 2003 to March 2015, systemic risk dramatically increased around the time of the recent global financial crisis and, to a lesser extent, around the time of the European debt crisis. BBVA played a predominant role as it both transmitted and received systemic risk to and from the remaining listed banks. Santander played a minor role and the smallest banks, Sabadell and Bankinter, did not play any pivotal role, not even between themselves. Finally, the main systemic impact of the Spanish banks on the European financial systems originated in BBVA, Popular and Santander, with the other listed banks playing a minor role in risk transmission. These results have implications for the regulation of capital in financial institutions and for investor risk management decisions.

As drought is among the natural hazards which affect people and economies world wide and often results in huge monetary losses, sophisticated methods for drought monitoring and decision making are needed. Many approaches to quantify drought severity have been developed during recent decades. However, most of these drought indices suffer from different shortcomings, account only for one or two driving factors which promote drought conditions and neglect their interdependences. We provide novel methodology for the calculation of (multivariate) drought indices, which combines the advantages of existing approaches and omits their disadvantages. It can be used flexibly in different applications to model different types of drought on the basis of user-selected, drought relevant variables.The methodology benefits from the flexibility of vine copulas in modelling multivariate non-Gaussian intervariable dependence structures. Based on a three-variate data set, an exemplary agrometeorological drought index is developed. The data analysis illustrates and reasons the methodology described. A validation of the exemplary multivariate agrometeorological drought index against observed soybean yield affirms the validity and abilities of the methodology. A comparison with established drought indices shows the benefits of our multivariate approach.

This paper attempts to model both static and dynamic dependence structures and measure impacts of energy consumptions (both renewable ( EC ) and non-renewable ( REN ) energies), economic globalization ( GLO ), and economic growth ( GDP ) on carbon dioxide ( CO 2 ) emissions in Argentina over the period 1970–2020. For analyses purpose, the current research deploys the novel static and dynamic copula-based ARIMA-fGARCH with different submodels. The static bivariate copula results show that the growth rates of the pairs EC - CO 2 and GDP - CO 2 are asymmetrically positive co-movements and have high left tail (extreme) dependencies, implying that the increase in non-renewable energy and economic growth can critically contribute to the environmental degradation, and the decrease in the consumption of non-renewable energy at a high level will consequently reduce the CO 2 emissions at the same level. Based on several copula-based dependence measures, we document that between the two factors, the non-renewable energy has a stronger impact than the economic growth regarding the CO 2 emissions. On the other hand, the growth rates of both economic globalization and renewable energy symmetrically negatively co-move with the growth rates of the CO 2 emissions, but they have no extreme dependencies, indicating that these factors contribute to Argentina’s environmental quality, in which the factor of renewable energy has a greater impact. Furthermore, the dynamic copula outcomes show that the (tail) dependencies of CO 2 emissions on the non-renewable energy and economic growth are time-varying, while the pairs REN - CO 2 and GLO - CO 2 possess only dynamic dependencies, but no dynamic tail dependencies. Moreover, through the dynamic copula-based dependence, the environmental Kuznets curve (EKC) hypothesis can be estimated and illustrated explicitly. In addition, we leverage multivariate vine copulas for modelling dependence structures of the five variables simultaneously, which can reveal rich information regarding conditional associations among the relevant variables. Some policy implications are also provided to mitigate CO 2 emissions.

Using only bivariate copulas as building blocks, regular vine copulas constitute a flexible class of high-dimensional dependency models. However, the flexibility comes along with an exponentially increasing complexity in larger dimensions. In order to counteract this problem, we propose using statistical model selection techniques to either truncate or simplify a regular vine copula. As a special case, we consider the simplification of a canonical vine copula using a multivariate copula as previously treated by Heinen & Valdesogo (2009) and Valdesogo (2009). We validate the proposed approaches by extensive simulation studies and use them to investigate a 19-dimensional financial data set of Norwegian and international market variables. En utilisant uniquement des copules bidimensionnelles comme unités de base, les copules en arborescence régulière constituent une classe flexible pour modéliser la dépendance pour les grandes dimensions. Toutefois, en grandes dimensions, la flexibilité s'accompagne d'une croissance exponentielle de la complexité. Pour contrecarrer ce problème, nous proposons l'utilisation des techniques de sélection de modèles statistiques afin de tronquer ou encore de simplifier la copule en arborescence régulière. Comme cas particulier, nous considérons la simplification de la copule en arborescence canonique par l'utilisation d'une copule multidimensionnelle telle que présentée dans Heinen et Valdesogo (2009) et Valdesogo (2009). Nous validons les approches proposées par de vastes études de simulation et nous les utilisons pour analyser un jeu de données financières de dimension 19 sur des variables des marchés norvégien et internationaux.

We introduce an extension of R-vine copula models to allow for spatial dependencies and model based prediction at unobserved locations. The proposed spatial R-vine model combines the flexibility of vine copulas with the classical geostatistical idea of modeling spatial dependencies using the distances between the variable locations. In particular, the model is able to capture non-Gaussian spatial dependencies. To develop and illustrate our approach, we consider daily mean temperature data observed at 54 monitoring stations in Germany. We identify relationships between the vine copula parameters and the station distances and exploit these in order to reduce the huge number of parameters needed to parametrize a 54-dimensional R-vine model fitted to 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.

The rise of new media is helping marketers evolve from digital to interactive marketing, which facilitates a two-way communication between marketers and customers without intruding on their privacy. However, while research has examined the drivers of customers' opt-in and opt-out decisions, it has investigated neither the timing of the two decisions nor the influence of transactional activity on the length of time a customer stays with an e-mail program. In this study, the authors adopt a multivariate copula model using a pair-copula construction method to jointly model opt-in time (from a customer's first purchase to the opt-in decision), optout time (from the opt-in decision to the opt-out decision), and average transaction amount. Through such multivariate dependences, this model significantly improves the predictive performance of the opt-out time in comparison with several benchmark models. The study offers several important findings: (1) marketing intensity affects opt-in and opt-out times, (2) customers with certain characteristics are more or less likely to opt in or opt out, and (3) firms can extend customer opt-out time and increase customer spending level by strategically allocating resources.