High Dimensional Forecasting via Interpretable Vector Autoregression
This work addresses forecasting challenges in multivariate time series for fields like economics, though it is incremental as it builds on existing regularized VAR methods.
The paper tackled the overparameterization problem in high-dimensional vector autoregression (VAR) models by proposing a new hierarchical lag structure (HLag) that embeds lag selection into a convex regularizer, resulting in improved forecasting performance and interpretable output, as demonstrated in simulations and a macroeconomic application.
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.