Authors: Martin Bladt and Alexander J. McNeil
Abstract: An approach to the modelling of volatile time series, such as financial returns, using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the marginal distribution and quantiles of the distribution of a predictable volatility proxy variable constructed as a function of the data. They permit a copula-based approach to volatile time series in which arbitrary marginal distributions may be combined with copula processes describing the serial dependence structure of the data. The idea is illustrated using stationary d-vine copula processes which model higher-order Markov dependence using a decomposition of the joint density into pair copulas. Estimation of the models can be carried out by maximum likelihood or by a sequential method-of-moments procedure using rank correlations. In combination with suitably-chosen parametric marginal distributions, it is shown that the resulting models can rival and often outperform well-known models in the extended GARCH family.