Modeling Non-Gaussian Stochastic Process with Bayesian Copula Method

• Activity Number: 433
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zhiguang Xu*+ and Steven MacEachern and Xinyi Xu
• Companies: The Ohio State University and Ohio State University and Ohio State University
• Keywords: copula ; non-Gaussian stochastic process ; nonparametric Bayesian method

Abstract

In linear regression where both response and covariates are observations from underlying continuous stochastic process, we expect the residuals to be time-dependent with non-Gaussian marginal distribution generally. We model this non-Gaussian residual process with a Bayesian copula method. This method has two components: (a) the nonparametric Bayesian method involving the modeling of the unknown distribution of stochastic process with a Mixture of Dirichlet Process which allows the flexibility of the shape of the distribution; (b) the Probability Integral Transformation (PIT) which enables us to model the stochastic process as the transformation of a Gaussian Process and characterize the dependence structure of the stochastic process. The non-Gaussian residual process is then completely specified through these two components. Theoretical results of this new method are discussed and this method is shown to provide better fit and forecast compared with the Gaussian competitors in simulations and financial data analysis.