Copula Modeling of Dependence in Multivariate Time Series

• Activity Number: 486
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Michael Smith*+
• Keywords: Copula ; Stationary ; Serial Dependence

Abstract

Almost all existing nonlinear multivariate time series models remain linear, conditional on a point in time or latent regime. Here, an alternative is proposed, where nonlinear serial and cross-sectional dependence is captured by a copula model. The copula defines a multivariate time series on the unit cube. A D-vine copula is employed, along with a factorization which allows the marginal and transitional densities of the time series to be expressed analytically. It also provides for simple conditions under which the series is stationary and/or Markov, as well as being parsimonious. A parallel algorithm for computing the likelihood is given, along with a Bayesian approach for computing inference based on model averages over parsimonious representations of the copula. The model average estimates are shown to be more accurate in a simulation study. Two five-dimensional time series from the Australian electricity market are examined. In both examples, the fitted copula captures substantial asymmetric tail dependence, both over time and across elements in the series