Modelling Volatile Returns with V-Transforms and Copulas

Summary

The paper presents a way to model volatile time series using v-transforms, which connect quantiles of a stationary series’ marginal distribution with quantiles of a predictable volatility proxy. Expressing these transforms as copulas lets the model combine flexible marginal distributions with a separate copula process governing volatility dynamics. The authors illustrate the framework with a Gaussian ARMA copula process and estimate it using an adaptation of exact maximum likelihood for ARMA models.

They report that the resulting model reproduces several stylized features of financial returns and supports calculation of marginal and conditional quantities, including quantile-based risk measures. In an empirical application to Bitcoin returns, the model is described as competitive with standard GARCH. The supplied description does not give the sample design, comparison metrics, or the precise features reproduced, so the strength and scope of that comparison cannot be assessed here. The results motivate the approach but do not establish that it will outperform GARCH in other markets or periods.

Key ideas

• V-transforms connect return quantiles to those of a predictable volatility proxy.
• A copula formulation allows marginal distributions to be combined with a process for volatility dynamics.
• The illustrated model uses a Gaussian ARMA copula process and an adapted exact maximum-likelihood estimator.
• The framework is used to derive conditional and marginal characteristics, including quantile risk measures.
• The Bitcoin application reports competitiveness with standard GARCH, while the supplied description omits comparison details.

Tags

# Modelling volatile time series with v-transforms and copulas


# Modelling volatile time series with v-transforms and copulas









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

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.