q-fin updates on arXiv.org
Tue, 25 Feb 2020 06:01:52 GMT language
An approach to the modelling of financial return series using a class of
uniformity-preserving transforms for uniform random variables is proposed.
V-transforms describe the relationship between quantiles of the return
distribution and quantiles of the distribution of a predictable volatility
proxy variable constructed as a function of the return. V-transforms can be
represented as copulas and permit the construction and estimation of models
that combine arbitrary marginal distributions with linear or non-linear time
series models for the dynamics of the volatility proxy. The idea is illustrated
using a transformed Gaussian ARMA process for volatility, yielding the class of
VT-ARMA copula models. These can replicate many of the stylized facts of
financial return series and facilitate the calculation of marginal and
conditional characteristics of the model including quantile measures of risk.
Estimation of models is carried out by adapting the exact maximum likelihood
approach to the estimation of ARMA processes.