Boosted p-Values for High-Dimensional Vector Autoregression

TL;DR

This paper introduces a method for computing valid p-values during the boosting process in high-dimensional vector autoregression, enabling better model selection and stability in complex time series analysis.

Contribution

It presents a novel approach to calculate asymptotically valid p-values at each boosting step, improving model selection and stability in high-dimensional VAR models.

Findings

P-values effectively control false positive rates in simulations.

Method produces sparser models with good prediction accuracy.

Assists in model stability and selection in macroeconomic data.

Abstract

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.