Variational Bayes Estimation of Time Series Copulas for Multivariate Ordinal and Mixed Data

• Activity Number: 400 - Recent Advances in Bayesian Computation and Modeling of High-Dimensional Multivariate Data
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael Stanley Smith* and Ruben Loaiza-Maya
• Companies: University of Melbourne and Unviersity of Melbourne
• Keywords: Copulas; Variational Bayes; Discrete Data

Abstract

We propose a new variational Bayes method for estimating high-dimensional copulas with discrete, or discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is substantially faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension rT, where T is the number of observation and r is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a common feature of ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. We illustrate using copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods.