Predictive assessment of copula models

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  • Author: Elif F. Acar, Parisa Azimaee and Md. Erfanul Hoque
  • Date: 19 April 2019
  • Copyright: Image copyright of Patrick Rhodes

Copulas are powerful explanatory tools for studying dependence patterns in multivariate data. While the primary use of copula models is in multivariate dependence modelling, they also offer predictive value for regression analysis. An article published in The Canadian Journal of Statistics investigates the utility of copula models for model‐based predictions from two angles. The authors assess whether, where, and by how much various copula models differ in their predictions of a conditional mean and conditional quantiles. From a model selection perspective, the authors then evaluate the predictive discrepancy between copula models using in‐sample and out‐of‐sample predictions both in bivariate and higher‐dimensional settings.

The paper is available with free access at the link here and the authors explain their findings below:

Predictive assessment of copula models

Elif F. Acar, Parisa Azimaee and Md. Erfanul Hoque

Volume 47, Issue 1, Special issue on Collaborative Research Team projects of the Canadian Statistical Sciences Institute

March 2019, pages 8-26

DOI: https://doi.org/10.1002/cjs.11468

thumbnail image: Predictive assessment of copula models

Correlation and regression are two central and inseparable concepts in statistics. The former quantifies the degree of association between two variables and the latter is used to make predictions of one variable given the value of the other. When the relationship between two variables is roughly linear, these foundational tools are very powerful and hard to beat. However, in many applications, variables exhibit relationships far more complex than linear, thus demanding more sophisticated statistical
approaches.

In this regard, copulas have emerged as a flexible and interpretable framework for capturing complex dependence relations that are invariant to the choice of marginal distributions. Advancing the notion of dependence beyond correlation, these models have been extensively studied in the context of multivariate dependence modelling and routinely applied to multivariate data to explain local dependence features, such as tail dependence. In light of the connection between correlation and regression, a natural question then is whether the increased flexibility of copula models in dependence modelling translates into better predictions in the regression setting.

This paper addresses this question by providing a detailed assessment of the predictive utility of copula models. A systematic evaluation of the bivariate case offers insight as to where copulas differ in their predictions, and when they provide added predictive value over the linear model. The paper further outlines a prediction-based approach to in-sample selection and out-of-sample evaluation of copula models, both in bivariate and higher dimensional settings. It is found that many copula models are difficult to distinguish in terms of overall predictive performance, with differences in predictions most apparent when conditioning on extreme events. More generally, the advantage of copula regression over linear modelling is greatest when the response is highly non-normal, the dependence is strongly non-elliptical, and predictions are targeted to tail regions.

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