Dimension Reduction for High Dimensional Vector Autoregressive Models

TL;DR

This paper introduces a dimension reduction technique for high-dimensional VAR models, decomposing them into a small VAR component and white noise, with methods for detection, estimation, and identifying key shocks in economic data.

Contribution

It extends the common feature approach to high-dimensional VARs, providing new statistical tools for decomposition, detection, and shock identification in large systems.

Findings

Successful decomposition of high-dimensional VARs into small VAR and noise.

Effective detection and estimation methods demonstrated through simulations.

Empirical application to US economic data identified key business cycle shocks.

Abstract

This paper aims to decompose a large dimensional vector autoregessive (VAR) model into two components, the first one being generated by a small-scale VAR and the second one being a white noise sequence. Hence, a reduced number of common components generates the entire dynamics of the large system through a VAR structure. This modelling, which we label as the dimension-reducible VAR, extends the common feature approach to high dimensional systems, and it differs from the dynamic factor model in which the idiosyncratic component can also embed a dynamic pattern. We show the conditions under which this decomposition exists. We provide statistical tools to detect its presence in the data and to estimate the parameters of the underlying small-scale VAR model. Based on our methodology, we propose a novel approach to identify the shock that is responsible for most of the common variability at the business cycle frequencies. We evaluate the practical value of the proposed methods by simulations as well as by an empirical application to a large set of US economic variables.