Abstract
An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family.11The analyses were carried out using R and the tscopula CRAN package, c.f (McNeil and Bladt, 2021), also available at https://github.com/ajmcneil/tscopula. In particular, it uses C++ code for vine copulas from the rvinecopulib package (Nagler and Vatter, 2020).
Highlights
The concept of a v-transform (McNeil, 2021) facilitates the application of copula models to time series where the dominant feature is stochastic volatility, such as financial asset return series
The contributions of the paper are threefold: we extend the theory of v-transformed copula processes as presented in McNeil (2021) to allow models that can describe both the phenomenon of stochastic volatility, as well as serial correlation in the direction of price movements; we show how to apply the modelling framework to copula processes based on d-vines and develop an approach to estimation; we demonstrate that the resulting models, when combined with suitable marginal distributions, can rival and sometimes outperform popular models in the GARCH class
The theory presented in the previous section can obviously be applied to the construction of time series copula processes (Ut)t∈Z that are suitable for modelling financial return data
Summary
The concept of a v-transform (McNeil, 2021) facilitates the application of copula models to time series where the dominant feature is stochastic volatility, such as financial asset return series. The contributions of the paper are threefold: we extend the theory of v-transformed copula processes as presented in McNeil (2021) to allow models that can describe both the phenomenon of stochastic volatility, as well as serial correlation in the direction of price movements; we show how to apply the modelling framework to copula processes based on d-vines and develop an approach to estimation; we demonstrate that the resulting models, when combined with suitable marginal distributions, can rival and sometimes outperform popular models in the GARCH class. We apply the fitted models to value-at-risk (VaR) estimation and analyse their outof-sample forecasting performance in Section 6; Section 7 concludes
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