Modelling Volatile Time Series with V-Transforms and Copulas

An approach to the modelling of volatile time series using a class uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe relationship between quantiles stationary distribution and predictable volatility proxy variable. They can be represented as copulas permit formulation estimation models that combine arbitrary marginal distributions with copula processes dynamics proxy. The idea illustrated Gaussian ARMA process resulting model shown replicate many stylized facts financial return facilitate calculation conditional characteristics including quantile measures risk. Estimation carried out by adapting exact maximum likelihood processes, competitive standard GARCH in an empirical application Bitcoin data.