High-Dimensional VARs with Common Factors

This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross-sectional dependence. Models of this type provide a convenient mechanism for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an ℓ1-nuclear-norm regularized estimator and derive the non-asymptotic upper bounds for the estimation errors as well as large sample asymptotics for the estimates. A singular value thresholding procedure is used to determine the correct number of factors with probability approaching one. Both the LASSO estimator and the conservative LASSO estimator are employed to improve estimation precision. The conservative LASSO estimates of the non-zero coefficients are shown to be asymptotically equivalent to the oracle least squares estimates. Simulations demonstrate that our estimators perform reasonably well in finite samples given the complex high-dimensional nature of the model. In an empirical illustration we apply the methodology to explore dynamic connectedness in the volatilities of financial asset prices and the transmission of ‘investor fear’. The findings reveal that a large proportion of connectedness is due to the common factors. Conditional on the presence of these common factors, the results still document remarkable connectedness due to the interactions between the individual variables, thereby supporting a common factor augmented VAR specification.