  Generalized autoregressive conditional heteroscedasticity (GARCH) models have
long been considered as one of the most successful families of approaches for
volatility modeling in financial return series. In this paper, we propose an
alternative approach based on methodologies widely used in the field of
statistical machine learning. Specifically, we propose a novel nonparametric
Bayesian mixture of Gaussian process regression models, each component of which
models the noise variance process that contaminates the observed data as a
separate latent Gaussian process driven by the observed data. This way, we
essentially obtain a mixture Gaussian process conditional heteroscedasticity
(MGPCH) model for volatility modeling in financial return series. We impose a
nonparametric prior with power-law nature over the distribution of the model
mixture components, namely the Pitman-Yor process prior, to allow for better
capturing modeled data distributions with heavy tails and skewness. Finally, we
provide a copula- based approach for obtaining a predictive posterior for the
covariances over the asset returns modeled by means of a postulated MGPCH
model. We evaluate the efficacy of our approach in a number of benchmark
scenarios, and compare its performance to state-of-the-art methodologies.
