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 factors generates the entire dynamics of the large system through a VAR structure. This modelling extends the common feature approach to high dimensional systems, and it differs from the dynamic factor models in which the idiosyncratic components can also embed a dynamic pattern. We show the conditions under which this decomposition exists , and we provide statistical tools to detect its presence in the data and to estimate the parameters of the underlying small-scale VAR model.  We evaluate the practical value of the proposed methodology by simulations as well as by empirical applications on both economic and financial time series .
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 factors generates the entire dynamics of the large system through a VAR structure. This modelling 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 .
R
models
model
R
components
component
R
, and we
. We
A
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.
R
methodology
methods
R
empirical applications on both economic and financial time series
an empirical application to a large set of US economic variables