Seasonal Quasi-Vector Autoregressive Models with an Application to Crude Oil Production and Economic Activity in the United States and Canada

We introduce the Seasonal-QVAR (quasi-vector autoregressive) model that we apply to study the relationship between oil production and economic activity. Seasonal-QVAR is a score-driven nonlinear model for the multivariate t distribution. It is an alternative to the basic structural model that disentangles local level and stochastic seasonality. Seasonal-QVAR is robust to extreme observations and it is an extension of Seasonal-VARMA (VAR moving average). We use monthly data from world crude oil production growth, global real economic activity growth and the industrial production growths of the United States and Canada. We address an important economic question about the influence of world crude oil production on the industrial productions of the United States and Canada. We find that the effects of industrial production growth of the United States on world crude oil production growth are about six times higher for the basic structural model and Seasonal-VARMA than for Seasonal-QVAR. We also find that the effects of world crude oil production growth on the industrial production growth of Canada are positive for Seasonal-QVAR, but those effects are negative for Seasonal-VARMA. Likelihood-based performance metrics and transitivity arguments support the estimates of Seasonal- QVAR, as opposed to the basic structural model and Seasonal-VARMA