Nonparametric Bayesian Modeling of Non-Gaussian Time Series with Conditional Heteroskedasticity

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zhiguang Xu*+ and Steven MacEachern and Xinyi Xu
• Companies: The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: Dirichlet Process ; GARCH ; copula

Abstract

An autoregressive (AR) model is frequently employed in modeling stationary time series. However, if the underlying marginal distribution of the observed data is non-Gaussian, then the AR model may yield poor fits and forecasts. We tackle this problem by applying the Probability Integral Transformation (PIT): the original series is assumed to have a marginal distribution of unknown form; we estimate this distribution using the Mixture Dirichlet Processes, and then transform the original series into a Gaussian AR series. The nonparametric Bayesian prior provides flexibility about the shape of the original series' distribution. Additionally, we embed a GARCH(1,1) structure in our model to capture the changes in volatility. The predictive densities based on our models are shown to effectively capture skewness, bimodality or leptokurtosis in the original series in both simulation studies and real data analysis; the model with the GARCH structure also captures the changes of volatility in the original series.