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.

In recent decades, substantial efforts have been devoted in flood monitoring, prediction, and risk analysis for aiding flood event preparedness plans and mitigation measures. Introducing an initial framework of spatially probabilistic analysis of flood research, this study highlights an integrated statistical copula and satellite data-based approach to modelling the complex dependence structures between flood event characteristics, i.e., duration (D), volume (V) and peak (Q). The study uses Global daily satellite-based Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) (spatial resolution of ∼5 km) during 1981–2019 to derive a Standardized Antecedence Precipitation Index (SAPI) and its characteristics through a time-dependent reduction function for Myanmar. An advanced vine copula model was applied to model joint distributions between flood characteristics for each grid cell. The southwest (Rakhine, Bago, Yangon, and Ayeyarwady) and south (Kayin, Mon, and Tanintharyi) regions are found to be at high risk, with a probability of up to 40% of flood occurrence in August and September in the south (Kayin, Mon, and Tanintharyi) and southwest regions (Rakhine, Bago, Yangon, and Ayeyarwady). The results indicate a strong correlation among flood characteristics; however, their mean and standard deviation are spatially different. The findings reveal significant differences in the spatial patterns of the joint exceedance probability of flood event characteristics in different combined scenarios. The probability that duration, volume, and peak concurrently exceed 50th-quantile (median) values are about 60–70% in the regions along the administrative borders of Chin, Sagaing, Mandalay, Shan, Nay Pyi Taw, and Keyan. In the worst case and highest risk areas, the probability that duration, volume, and peak exceed the extreme values, i.e., the 90th-quantile, about 10–15% in the southwest of Sagaing, southeast of Chin, Nay Pyi Taw, Mon and areas around these states and up to 30% in the southeast of Dekkhinathiri township (Nay Pyi Taw). The proposed approach could improve the evaluation of exceedance probabilities used for flood early warning and risk assessment and management. The proposed framework is also applicable at larger scales (e.g., regions, continents and globally) and in different hydrological design events and for risk assessments (e.g., insurance).

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. The new model class is illustrated by an application to forecasting returns of a portfolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation.