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Variational Bayes estimation of discrete-margined copula models with application to time series

Mar 22, 2019 11:00 am - 12:00 pm AEDT

Abstract
We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is 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 observations 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 feature of most 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. Using six example series, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for 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. An Online Appendix and MATLAB code implementing the method are available as Supplementary Materials.

This work is joint with Ruben Loaiza-Maya from Melbourne Business School from the University of Melbourne.

Bio
Michael Smith has held the Chair of Management in Econometrics at Melbourne Business School since 2007, and is also an Honorary Professor of Business Analytics at the University of Sydney. He is a leading researcher in Bayesian statistics and business analytics.

Michael’s research focuses on developing methods for the analysis of large and complex datasets that arise in business, economics and elsewhere. On the methodological side, he has worked on Bayesian algorithms, spatial and time series analysis and multivariate modelling. On the applied side, he has worked on marketing models for advertising effectiveness and consumer response, neuroimaging, and macroeconomic and business forecasting. He has a long-standing interest in the electricity markets, including the modelling and forecasting of demand and spot prices. Michael’s research has been published widely in the leading academic journals in statistics, econometrics, marketing and forecasting.

Dr Chao Wang
T +61 2 9036 9101
E chao.wang@sydney.edu.au