  A factor-augmented vector autoregressive (FAVAR) model is defined by a VAR
equation that captures lead-lag correlations amongst a set of observed
variables $X$ and latent factors $F$, and a calibration equation that relates
another set of observed variables $Y$ with $F$ and $X$. The latter equation is
used to estimate the factors that are subsequently used in estimating the
parameters of the VAR system. The FAVAR model has become popular in applied
economic research, since it can summarize a large number of variables of
interest as a few factors through the calibration equation and subsequently
examine their influence on core variables of primary interest through the VAR
equation. However, there is increasing need for examining lead-lag
relationships between a large number of time series, while incorporating
information from another high-dimensional set of variables. Hence, in this
paper we investigate the FAVAR model under high-dimensional scaling. We
introduce an appropriate identification constraint for the model parameters,
which when incorporated into the formulated optimization problem yields
estimates with good statistical properties. Further, we address a number of
technical challenges introduced by the fact that estimates of the VAR system
model parameters are based on estimated rather than directly observed
quantities. The performance of the proposed estimators is evaluated on
synthetic data. Further, the model is applied to commodity prices and reveals
interesting and interpretable relationships between the prices and the factors
extracted from a set of global macroeconomic indicators.
