Dimension Reduction for High Dimensional Vector Autoregressive Models

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.