Examination and visualisation of the simplifying assumption for vine copulas in three dimensions

Killiches, Matthias; Kraus, Daniel; Czado, Claudia

doi:10.1111/anzs.12182

Cited by 37 publications

(20 citation statements)

References 33 publications

(70 reference statements)

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“…Copulas functions are able to capture the dependence structure separately from their marginal distributions (Yin et al, ). Regular vine copulas further extend the dependence model to the multivariate framework by building a hierarchical set of bivariate and conditional bivariate copulas (Killiches et al, ). Z Liu et al () developed a streamflow prediction model using the conditional functions of canonical vine copulas to generate streamflow of 1 month ahead.…”

Section: Introductionmentioning

confidence: 99%

Monthly Streamflow Simulation for the Headwater Catchment of the Yellow River Basin With a Hybrid Statistical‐Dynamical Model

Wang

Dong

Lall

et al. 2019

Water Resources Research

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Streamflow simulation of the headwater catchment of the Yellow River basin (HCYRB) in China is important for water resources management of the Yellow River basin. A statistical‐dynamical model, combining regular vine copulas with an optimization method for structure estimation, is presented with an application for simulating the monthly streamflow with local climate drivers at HCYRB. Local climate drivers for streamflow in every month are analyzed using rank‐based correlation. Precipitation, evaporation, and temperature generally show strong associations with streamflow. Winter streamflows relate to total precipitation of the wet season and total evaporation of October and November, while unfrozen‐month streamflows are correlated with evaporation and precipitation of current month and previous 1 month in the wet season. Both canonical vine and D‐vine copulas are applied to develop different conditional quantile functions for streamflows in different months with their dynamical covariates. The covariates are selected from historical streamflows and climate drivers with appropriate lags using partial correlations. The optimal vine trees are selected using the sequential maximum spanning tree algorithm with the weight based on both dependence and goodness of fit. The model demonstrates higher skill than existing vine‐based models and the seasonal autoregressive integrated moving average model. The enhanced skill of the hybrid statistical‐dynamical model comes from an improved capability of capturing nonlinear correlation and tail dependence of streamflow and climate drivers with the optimization of vine structure selection. The model provides an effective advance to enhance water resources planning and management for HCYRB and the whole basin.

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Section: Introductionmentioning

confidence: 99%

Monthly Streamflow Simulation for the Headwater Catchment of the Yellow River Basin With a Hybrid Statistical‐Dynamical Model

Wang

Dong

Lall

et al. 2019

Water Resources Research

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“…The work in [13] shows that the approximation in fact may be a good one, even when the simplifying assumption is far from being fulfilled. This subject has also been investigated by Stöber et al [14], Killiches et al [15] and Spanhel and Kurz [16].…”

Section: Simplifying Assumptionmentioning

confidence: 88%

Pair-Copula Constructions for Financial Applications: A Review

Aas

2016

Econometrics

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This survey reviews the large and growing literature on the use of pair-copula constructions (PCCs) in financial applications. Using a PCC, multivariate data that exhibit complex patterns of dependence can be modeled using bivariate copulae as simple building blocks. Hence, this model represents a very flexible way of constructing higher-dimensional copulae. In this paper, we survey inference methods and goodness-of-fit tests for such models, as well as empirical applications of the PCCs in finance and economics.

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“…The data set contains 655 observations which measure the log-concentration of 7 chemicals in water samples from the Montrose quadrangle of western Colorado. This particular data set is often discussed in articles related to copulas, see for instance Gijbels et al (2012) or Killiches et al (2016) who both investigate the simplifying assumption for three-dimensional subsets. Both studies detect that a non-simplified vine copula improves the fit of the data subset.…”

Section: Application: Uranium Data Setmentioning

confidence: 99%

Estimating non-simplified vine copulas using penalized splines

Schellhase

Spanhel

2017

Stat Comput

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Vine copulas (or pair-copula constructions) have become an important tool for highdimensional 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 non-parametric 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.

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Examination and visualisation of the simplifying assumption for vine copulas in three dimensions

Cited by 37 publications

References 33 publications

Monthly Streamflow Simulation for the Headwater Catchment of the Yellow River Basin With a Hybrid Statistical‐Dynamical Model

Monthly Streamflow Simulation for the Headwater Catchment of the Yellow River Basin With a Hybrid Statistical‐Dynamical Model

Pair-Copula Constructions for Financial Applications: A Review

Estimating non-simplified vine copulas using penalized splines

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