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Title: Gaussian process-mixture conditional heteroscedasticity
Authors: Platanios, Emmanouil Antonios 
Chatzis, Sotirios P. 
Keywords: Gaussian process;Pitman-Yor process;Mixture model;Conditional heteroscedasticity;Copula;Volatility modeling
Category: Mathematics
Field: Natural Sciences
Issue Date: May-2014
Publisher: IEEE
Source: IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, Volume 36, Issue 5, Pages 888-900
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 Gaussian process-mixture conditional heteroscedasticity (GPMCH) 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 GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.
ISSN: 0162-8828
DOI: 10.1109/TPAMI.2013.183
Rights: © IEEE
Type: Article
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