Forecasting Medium and Large Datasets with Vector Autoregressive Moving Average (VARMA) Models

We address the issue of modelling and forecasting macroeconomic variables using medium and large datasets, by adopting VARMA models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for strong and weak VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models outperform the AR(1), VAR(p) and factor models, considering different model dimensions.