Abstract
Based on (different) bivariate copulas as simple building blocks to model complex multivariate dependency patterns, vine copulas provide flexible multivariate models. They, however, lose their flexibility with dimensions. Attempts have been existing to reduce the model complexity by searching for a subclass of truncation vine copulas, of which only a limited number of vine trees are estimated. However, they are either time-consuming or model-dependent or require additional computational efforts. Inspired by the relationship between copula’s parameters (and the corresponding Kendall’s tau) and the mutual information on the one side and the mutual information and copula entropy on another side, this study proposed a novel truncation vine copula model using only mutual information values among variables. This newly proposed truncation method is evaluated in simulation studies and a real application of financial returns dataset. The simulated and real studies show that the model is sufficiently good to find the most appropriate truncation level with a good fit of a given data.
Highlights
Copula models have become a popular statistical dependence modeling tool in the literature. ey gain their flexibility from(1) allowing modeling univariate marginal distribution functions independently from modeling the dependency patterns among variables and (2) modeling a wide range of complex nonlinear dependency patterns among variables
In this study, inspired by the work of [14, 15] and build on the work of [16], we develop a novel and ever flexible model-independent truncation approach to solve the problem of selecting the truncation level of the regular vine (R-vine) copula model. e newly introduced model is solely based on the mutual information values among variables and, does not require the selection and estimation of paircopulas
The result of listing 1 verifies that truncating the model at level 3 explains the data well. us, the contribution of 66 bivariate copulas at levels 4 :14 is minor. erefore, our model provides a more parsimonious subclass vine copula model, yet still offers a good fit for the data. e contour plot of the fitted copula is shown in Figure 2, which supports the results of our newly proposed truncation approach
Summary
Copula models have become a popular statistical dependence modeling tool in the literature. ey gain their flexibility from(1) allowing modeling univariate marginal distribution functions independently from modeling the dependency patterns among variables and (2) modeling a wide range of complex nonlinear dependency patterns among variables. E authors illustrate that their newly proposed estimation method of the truncation level provides a much better result in comparison with [11] Their approach requires, for each tree, selecting the best minimum spanning tree for each previous tree among a large number of possible candidates. In comparison with Kendall’s tau-based method, the author illustrates that the MI-based approach provided more information on the variables For truncation purpose, they apply the idea of [11] using AIC. Us, this study contributes significantly to the current state of the art by providing an optimising and extreme flexible modelindependent truncation method to dramatically reduce the complex computation of a high-dimensional dataset and yet still provide a good model-fit to the underlying data. Ni et al [16] showed that CMI can be expressed as a weighted average of the negative conditional CE
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