We develop statistical tools for time series analysis of high-dimensional multivariate datasets, when a few core series are of principal interest and there are many potential ancillary predictive variables. The methodology, based on Vector Autoregressions (VAR), handles the case where unrestricted fitting is precluded by the large number of series and a huge parameter space. In particular, we adopt a forecast error criterion and use Granger-causality tests in a sequential manner to build a VAR model that targets the main variables. This approach effects variable reduction (or equivalently, sparsity restrictions) in a computationally fast way that remains feasible for high dimensions. The search for the best model results in a VAR, fitted with a selection of supporting series, that has the best possible forecast performance with respect to the core variables. We apply the statistical methodology to model real Gross Domestic Product and the national Unemployment Rate, two time series widely monitored by economists and policy-makers, based on a large set of Quarterly Workforce Indicators comprising various major sectors of the economy and different measures of labor market conditions.