Hierarchical Vector Autoregression

• Activity Number: 310
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): William B. Nicholson* and David S. Matteson and Jacob Bien
• Companies: Cornell University and Cornell University and Cornell University
• Keywords: Multivariate Time Series ; Hierarchical Group Lasso ; Dimension Reduction ; Sparsity ; High Dimensional Time Series ; Forecasting

Abstract

Vector autoregression (VAR) is a fundamental tool for modeling the joint dynamics of multivariate time series. However, as the number of series is increased, the VAR model quickly becomes overparameterized. Traditional approaches attempt to address overparameterization by selecting a low commmon lag order. While having a common lag reduces the computational complexity of model selection, it constrains the relationship between the components and impedes forecast performance. We propose a new class of regularized VAR models, called hierarchical vector autoregression (HVAR), that embed the notion of lag selection into a convex regularizer. The key modeling tool is a group lasso with hierarchically nested groups which guarantees that the sparsity pattern of autoregressive lag coefficients honors the ordered structure inherent to VAR. We focus on three structures within the HVAR class, which allow for varying levels of flexibility. A simulation study shows improved performance in forecasting and lag order selection over previous approaches, and a macroeconomic application further highlights forecasting improvements as well as the convenient, interpretable output of a HVAR model.