Inverse Wishart Autoregressive Processes

• Activity Number: 638
• Type: Invited
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Emily Fox*+ and Mike West
• Companies: Duke University and Duke University
• Keywords: time series ; covariance processes ; autoregressive processes ; Bayesian

Abstract

Modeling the temporal dependencies of high-dimensional covariance matrices has become a growing focus in the development multi- and matrix-variate time series methodology, with applications in fields as diverse as econometrics, neuroscience, epidemiology, and the more general area of spatial-temporal modeling. The covariance matrix captures the key correlations between the time series, and the typical assumption of a time-homogenous covariance can have significant impact on inferences. We introduce a rich class of stationary time series models for covariance matrices that extend classical autoregressive processes to the cone of positive semi-definite matrices. The theory and structure of these novel AR models for multivariate "volatility" processes will be described, as will simulation methods for Bayesian computations in these models. Applications to EEG time series demonstrate their utility.