Longitudinal Data Analysis and Time Series Commons^™

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this paper, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, …