Dimension Reduction for High Dimensional Vector Autoregressive Models

31 Pages Posted: 25 Mar 2022

See all articles by Gianluca Cubadda

Gianluca Cubadda

University of Rome Tor Vergata - Department of Economics and Finance

Alain Hecq

Maastricht University - Department of Quantitative Economics

Date Written: March 24, 2022

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.

Keywords: Vector autoregressive models, dimension reduction, reduced-rank regression, multivariate autoregressive index model, common features, business cycle shock.

Suggested Citation

Cubadda, Gianluca and Hecq, Alain, Dimension Reduction for High Dimensional Vector Autoregressive Models (March 24, 2022). CEIS Working Paper No. 534, Available at SSRN: https://ssrn.com/abstract=4065810 or http://dx.doi.org/10.2139/ssrn.4065810

Gianluca Cubadda (Contact Author)

University of Rome Tor Vergata - Department of Economics and Finance ( email )

Via Columbia n.2
Roma, 00133
Italy

Alain Hecq

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://www.maastrichtuniversity.nl/a.hecq

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