Modelling multivariate ordinal time series using pairwise likelihood

Abstract: We assume that we have multiple ordinal time series and we would like to specify their joint distribution. In general it is difficult to create multivariate distribution that can be easily used to jointly model ordinal variables and the problem becomes even more complex in the case of time series, since we have to take into consideration not only the autocorrelation of each time series and the dependence between time series, but also cross-correlation. Starting from the simplest case of two ordinal time series, we propose using copulas to specify their joint distribution. We extend our approach in higher dimensions, by approximating full likelihood with composite likelihood and especially conditional pairwise likelihood, where each bivariate model is specified by copulas. We suggest maximizing each bivariate model independently to avoid computational issues and synthesize individual estimates using weighted mean. Weights are related to the Hessian matrix of each bivariate model. Simulation studies showed that model fits well under different sample sizes. Forecasting approach is also discussed. A small real data application about unemployment state of different countries of European Union is presented to illustrate our approach.