High Dimensional Time-varying Parameter Vector Autoregressions

We propose to estimate high dimensional time-varying parameter vector autoregressive (VAR) models using a frequentist approach which combines a dynamic factor model and l1-regularization, instead of the traditional Bayesian approach. We develop the two-step coordinate descent (TSCD) algorithm to solve this nonstandard optimization problem. It is a conceptually very simple sequential algorithm based on the coordinate descent (CD) algorithm and the Kalman Filter. Simulation studies show the good performance of our algorithm in various scenarios. Moreover, the TSCD algorithm is computationally very efficient and easy to implement. Using the FRED-QD dataset on US macroeconomic and financial variables we show that the approach is promising in estimating a small and high dimensional time-varying parameter VAR model which have previously been studied in a Bayesian framework.