Copulae: An overview and recent developments

Größer, Joshua; Okhrin, Ostap

doi:10.1002/wics.1557

Cited by 12 publications

(9 citation statements)

References 164 publications

(194 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Copula modeling, similar to any other modeling effort, is associated with uncertainties (e.g., due to insufficient observations or model structural uncertainty), which propagate into joint probability estimates and other derived inferences (Sadegh et al, 2018). Additional challenges for the practical application of copulas, apart from uncertainty, have also stimulated currently trending research focusing, for instance, on (1) Vine copulas to construct higher‐dimensional copulas , for example, to assess interplay between three or more hydroclimatic variables (Aas et al, 2009; Größer & Okhrin, 2021; Pham et al, 2016; W. Wang et al, 2019), (2) dynamic copulas for retaining autocorrelation and nonstationarity in hydroclimatic time series (Ahn & Palmer, 2016; Feng et al, 2020; Rakonczai et al, 2012), and (3) copula modeling for hydroclimatic data with ties (Kojadinovic, 2017; Y. Li et al, 2020).…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Copulas for hydroclimatic analysis: A practice‐oriented overview

et al. 2022

View full text Add to dashboard Cite

A warming climate is associated with increasing hydroclimatic extremes, which are often interconnected through complex processes, prompting their concurrence and/or succession, and causing compound extreme events. It is critical to analyze the risks of compound events, given their disproportionately high adverse impacts. To account for the variability in two or more hydroclimatic variables (e.g., temperature and precipitation) and their dependence, a rising number of publications focuses on multivariate analysis, among which the notion of copula‐based probability distribution has attracted tremendous interest. Copula is a mathematical function that expresses the joint cumulative probability distribution of multiple variables. Our focus is to re‐emphasize the fundamental requirements and limitations of applying copulas. Confusion about these requirements may lead to misconceptions and pitfalls, which can potentially compromise the robustness of risk analyses for environmental processes and natural hazards. We conducted a systematic literature review of copulas, as a prominent tool in the arsenal of multivariate methods used for compound event analysis, and underpinned them with a hydroclimatic case study in Sweden to illustrate a practical approach to copula‐based modeling. Here, we (1) provide end‐users with a didactic overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) synthesize common perceptions and practices, and (3) offer a user‐friendly decision support framework to employ copulas, thereby support researchers and practitioners in addressing hydroclimatic hazards, hence demystify what can be an area of confusion. This article is categorized under: Science of Water > Hydrological Processes Science of Water > Methods

show abstract

Section: Discussionmentioning

confidence: 99%

“…However, the mathematical procedure to obtain these copulas are generally more complex, and further uncertainties may emerge (Rakonczai et al, 2012). For more information and an advanced review of copulas for autocorrelated time series, the reader is referred to Größer and Okhrin (2021), Oh and Patton (2018), and Patton (2006, 2012).…”

Section: Introductionmentioning

confidence: 99%

Copulas for hydroclimatic analysis: A practice‐oriented overview

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Copula enables us to model the multivariate distribution of random variables by separating the marginal distribution and dependency structure of these margins. For recent developments in the field of the copula, the interested reader can refer to [43].…”

Section: Modelling the Dependencymentioning

confidence: 99%

Importance of Weather Conditions in a Flight Corridor

Chen

Fricke

Okhrin

et al. 2022

Stats

Self Cite

View full text Add to dashboard Cite

Current research initiatives, such as the Single European Sky Air Traffic Management Research Program, call for an air traffic system with improved safety and efficiency records and environmental compatibility. The resulting multi-criteria system optimization and individual flight trajectories require, in particular, reliable three-dimensional meteorological information. The Global (Weather) Forecast System only provides data at a resolution of around 100 km. We postulate a reliable interpolation at high resolution to compute these trajectories accurately and in due time to comply with operational requirements. We investigate different interpolation methods for aerodynamic crucial weather variables such as temperature, wind speed, and wind direction. These methods, including Ordinary Kriging, the radial basis function method, neural networks, and decision trees, are compared concerning cross-validation interpolation errors. We show that using the interpolated data in a flight performance model emphasizes the effect of weather data accuracy on trajectory optimization. Considering a trajectory from Prague to Tunis, a Monte Carlo simulation is applied to examine the effect of errors on input (GFS data) and output (i.e., Ordinary Kriging) on the optimized trajectory.

show abstract

“…Researchers from different fields recognize the power of copulae while working with multivariate datasets from insurance (Fang and Madsen, 2013;Shi et al, 2016), finance (Salvatierra and Patton, 2015;Oh and Patton, 2018), biology (Konigorski et al, 2014;Dokuzoglu and Purutçuoglu, 2017), hydrology (Liu et al, 2018;Valle and Kaplan, 2019), medicine (Kuss et al, 2014;Gomes et al, 2019), traffic engineering, (Huang et al, 2017;Ma et al, 2017), etc. For a recent review, we refer to Größer and Okhrin (2021). Unfortunately, the correct specification of the multivariate distribution is not easy to find, and often interest in the understanding of the functional form of the copula is dominated by the expected performance of the whole model.…”

Section: Introductionmentioning

confidence: 99%

gofCopula: Goodness-of-Fit Tests for Copulae

Okhrin¹,

Trimborn²,

Waltz³

2021

The R Journal

Self Cite

View full text Add to dashboard Cite

The last decades show an increased interest in modeling various types of data through copulae. Different copula models have been developed, which lead to the challenge of finding the best fitting model for a particular dataset. From the other side, a strand of literature developed a list of different Goodness-of-Fit (GoF) tests with different powers under different conditions. The usual practice is the selection of the best copula via the p-value of the GoF test. Although this method is not purely correct due to the fact that non-rejection does not imply acception, this strategy is favored by practitioners. Unfortunately, different GoF tests often provide contradicting outputs. The proposed R-package brings under one umbrella 13 most used copulae -plus their rotated variants -together with 16 GoF tests and a hybrid one. The package offers flexible margin modeling, automatized parallelization, parameter estimation, as well as a user-friendly interface, and pleasant visualizations of the results. To illustrate the functionality of the package, two exemplary applications are provided.

show abstract

Copulae: An overview and recent developments

Cited by 12 publications

References 164 publications

Copulas for hydroclimatic analysis: A practice‐oriented overview

Copulas for hydroclimatic analysis: A practice‐oriented overview

Importance of Weather Conditions in a Flight Corridor

gofCopula: Goodness-of-Fit Tests for Copulae

Contact Info

Product

Resources

About