Mixture Gaussian Process Conditional Heteroscedasticity

TL;DR

This paper introduces a novel nonparametric Bayesian mixture of Gaussian process models for volatility estimation in financial data, capturing heavy tails and skewness more effectively than traditional GARCH models.

Contribution

It proposes a mixture Gaussian process conditional heteroscedasticity (MGPCH) model with a Pitman-Yor prior, enhancing volatility modeling with nonparametric Bayesian methods.

Findings

Outperforms traditional GARCH models in benchmark tests

Effectively captures heavy tails and skewness in financial data

Provides a copula-based approach for covariance prediction

Abstract

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.