  Assessing the statistical significance of parameter estimates is an important
step in high-dimensional vector autoregression modeling. Using the
least-squares boosting method, we compute the p-value for each selected
parameter at every boosting step in a linear model. The p-values are
asymptotically valid and also adapt to the iterative nature of the boosting
procedure. Our simulation experiment shows that the p-values can keep false
positive rate under control in high-dimensional vector autoregressions. In an
application with more than 100 macroeconomic time series, we further show that
the p-values can not only select a sparser model with good prediction
performance but also help control model stability. A companion R package
boostvar is developed.
