Copula modelling of dependence in multivariate time series

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 drawable vine copula is employed, along with a factorization which allows the marginal and transitional densities of the time series to be expressed analytically. The factorization 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 proposed, along with a Bayesian approach for computing inference based on model averages over parsimonious representations of the vine 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 a substantial level of asymmetric tail dependence, both over time and between elements in the series.