kdecopula: An R Package for the Kernel Estimation of Bivariate Copula Densities

We describe the R package kdecopula (current version 0.9.2), which provides fast implementations of various kernel estimators for the copula density. Due to a variety of available plotting options it is particularly useful for the exploratory analysis of dependence structures. It can be further used for accurate nonparametric estimation of copula densities and resampling. The implementation features spline interpolation of the estimates to allow for fast evaluation of density estimates and integrals thereof. We utilize this for a fast renormalization scheme that ensures that estimates are bona fide copula densities and additionally improves the estimators' accuracy. The performance of the methods is illustrated by simulations

Vine copula approximation : a generic method for coping with conditional dependence

Pair-copula constructions (or vine copulas) are structured, in the layout of vines, with bivariate copulas and conditional bivariate copulas. The main contribution of the current work is an approach to the long-standing problem: how to cope with the dependence structure between the two conditioned variables indicated by an edge, acknowledging that the dependence structure changes with the values of the conditioning variables. This problem is known as the non-simplified vine copula modelling and, though recognized as crucial in the field of multivariate modelling, remains widely unexplored due to its inherent complication, and hence is the motivation of the current work. Rather than resorting to traditional parametric or non-parametric methods, we proceed from an innovative viewpoint: approximating a conditional copula, to any required degree of approximation, by utilizing a family of basis functions. We fully incorporate the impact of the conditioning variables on the functional form of a conditional copula by employing local learning methods. The attractions and dilemmas of the pair-copula approximating technique are revealed via simulated data, and its practical importance is evidenced via a real data set

Testing the simplifying assumption in high-dimensional vine copulas

Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and amount to checking constraints on high-dimensional distributions. So far, corresponding tests have been limited to single conditional copulas with a low-dimensional set of conditioning variables. We propose a novel testing procedure that is computationally feasible for high-dimensional data sets and that exhibits a power that decreases only slightly with the dimension. By discretizing the support of the conditioning variables and incorporating a penalty in the test statistic, we mitigate the curse of dimensions by looking for the possibly strongest deviation from the simplifying assumption. The use of a decision tree renders the test computationally feasible for large dimensions. We derive the asymptotic distribution of the test and analyze its finite sample performance in an extensive simulation study. The utility of the test is demonstrated by its application to six data sets with up to 49 dimensions

Dependence modeling with applications in financial econometrics

The amount of data available in banking, finance and economics steadily increases due to the ongoing technological progress and the continuing digitalization. A key element of many econometric models for analyzing this data are methods for assessing dependencies, cross-sectionally as well as intertemporally. For this reason, the thesis is centered around statistical and econometric methods for dependence modeling with applications in financial econometrics. The first part of this cumulative dissertation consists of three contributions. The first contribution provides a thorough explanation of the partial copula. It is a natural generalization of the partial correlation coefficient and several of its properties are investigated. In the second contribution, a different multivariate generalization of the partial correlation, the partial vine copula (PVC), is introduced. The PVC is a specific simplified vine copula (SVC) consisting of bivariate higher-order partial copulas, which are copula-based generalizations of sequentially computed partial correlations. Several properties of the PVC are presented and it is shown that, if SVCs are considered as approximations of multivariate distributions, the PVC has a special role as it is the limit of stepwise estimators. The third contribution introduces statistical tests for the simplifying assumption with a special focus on high-dimensional vine copulas. We propose a computationally feasible test for the simplifying assumption in high-dimensions, which is successfully applied to data sets with up to 49 dimensions. The novel test procedure is based on a decision tree which is used to identify the possibly strongest violation of the simplifying assumption. The asymptotic distribution of the test statistic is derived under consideration of estimation uncertainty in the copula parameters. The finite sample performance is analyzed in an extensive simulation study and the results show that the power of the test only slightly decreases in the dimensionality of the test problem. In the second part of the dissertation, the assessment of risk measures is studied with a special focus on the financial return data used for estimation. It is shown that the choice of the sampling scheme can greatly affect the results of risk assessment procedures if the assessment frequency and forecasting horizon are fixed. Specifically, we study sequences of variance estimates and show that they exhibit spurious seasonality, if the assessment frequency is higher than the sampling frequency of non-overlapping return data. The root cause of spurious seasonality is identified by deriving the theoretical autocorrelation function of sequences of variance estimates under general assumptions. To overcome spurious seasonality, alternative variance estimators based on overlapping return data are suggested. The third part of the dissertation is about state space methods for systems with lagged states in the measurement equation. Recently, a low-dimensional modified Kalman filter and smoother for such systems was proposed in the literature. Special attention is paid to the modified Kalman smoother, for which it is shown that the suggested smoother in general does not minimize the mean squared error (MSE). The correct MSE-minimizing modified Kalman smoother is derived and computationally more efficient smoothing algorithms are discussed. Finally, a comparison of the competing smoothers with regards to the MSE is performed

Description Flexible Pair-Copula Estimation in D-vines using Bivariate Penalized Splines. License GPL (> = 2)

R topics documented: penDvine-package..................................... 2 bernstein........................................... 3 cal.Dvine.......................................... 4 cond.cop........................................... 4 Derv1............................................