  Vector autoregression (VAR) is a fundamental tool for modeling multivariate
time series. However, as the number of component series is increased, the VAR
model becomes overparameterized. Several authors have addressed this issue by
incorporating regularized approaches, such as the lasso in VAR estimation.
Traditional approaches address overparameterization by selecting a low lag
order, based on the assumption of short range dependence, assuming that a
universal lag order applies to all components. Such an approach constrains the
relationship between the components and impedes forecast performance. The
lasso-based approaches work much better in high-dimensional situations but do
not incorporate the notion of lag order selection.
  We propose a new class of hierarchical lag structures (HLag) that embed the
notion of lag selection into a convex regularizer. The key modeling tool is a
group lasso with nested groups which guarantees that the sparsity pattern of
lag coefficients honors the VAR's ordered structure. The HLag framework offers
three structures, which allow for varying levels of flexibility. A simulation
study demonstrates improved performance in forecasting and lag order selection
over previous approaches, and a macroeconomic application further highlights
forecasting improvements as well as HLag's convenient, interpretable output.
