GARCH copulas, v-transforms and d-vines

Seminar in Insurance and Economics

SPEAKER: Alexander McNeil (University of York).

TITLE: GARCH copulas, v-transforms and d-vines.

ABSTRACT: Stationary models from the GARCH class have proved to be extremely useful for forecasting volatility and measuring risk in financial time series. However, the nature of their implied copulas is opaque. We analyse the serial dependence structure of first-order GARCH-type models in terms of the implied bivariate copulas that describe the dependence and partial dependence of pairs of variables at different lags. Our aim is to understand whether such dependence structures could be mimicked with appropriately chosen bivariate copulas arranged in d-vines. We find that uniformity-preserving transformations, known as v-transforms, are implicitly embedded in the copulas of classical GARCH models and we propose that they could be used as explicit modelling elements to construct vine copulas for applications. Our aim is to develop more flexible models that can improve upon the GARCH class in situations where the latter does not work well. Our results suggest that d-vine models with appropriately chosen pair copulas can rival and often surpass the performance of GARCH processes for many volatile financial return series.

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