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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. 

In a number of applications, one has access to high-dimensional time series data on several related subjects. A motivating application area comes from the neuroimaging field, such as brain fMRI time series data, obtained from various groups of subjects (cases/controls) with a specific neurological disorder. The problem of regularized joint estimation of multiple related Vector Autoregressive (VAR) models is discussed, leveraging a group lasso penalty in addition to a regular lasso one, so as to increase statistical efficiency of the estimates by borrowing strength across the models. A modeling framework is developed that it allows for both group-level and subject-specific effects for related subjects, using a group lasso penalty to estimate the former. An estimation procedure is introduced, whose performance is illustrated on synthetic data and compared to other state-of-the-art methods. Moreover, the proposed approach is employed for the analysis of resting state fMRI data. In particular, a group-level descriptive analysis is conducted for brain inter-regional temporal effects of Attention Deficit Hyperactive Disorder (ADHD) patients as opposed to controls, with the data available from the ADHD-200 Global Competition repository.