High Dimensional Forecasting via Interpretable Vector Autoregression

TL;DR

This paper introduces HLag, a hierarchical regularization method for high-dimensional VAR models that improves forecasting accuracy and interpretability by embedding lag selection into the model structure.

Contribution

The paper proposes a novel hierarchical lag regularizer for VAR models that integrates lag selection into the estimation process, enhancing forecast performance and interpretability.

Findings

HLag outperforms existing methods in simulation studies.

HLag improves macroeconomic forecast accuracy.

HLag provides interpretable lag structures.

Abstract

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.