Model Selection for Vector Autoregressive processes using the Multi-Step Elastic Net

Several penalized variable estimation techniques such as the (adaptive) elastic net have been proposed for modeling VAR data in order to improve dimension reduction and forecast performance. Literature has proven that the multi-step adaptive elastic net gains in sparsity performance, however, this has never been investigated within a VAR framework. The aim is therefore to analyze if the multi-step adaptive elastic net (maenet) is able to provide the accurate VAR model compared to its single step variants used as benchmark methods such as the elastic net (enet), adaptive elastic net with ridge weights (aenetR) and the adaptive elastic net with lasso weights (aenetL). I compare them in terms of estimation bias, sparsity and forecast performance. Simulation results show that the multi-step adaptive elastic net is able to consistently find sparser VAR models compared to the benchmark methods with a gain in efficiency and accuracy as the probability of selecting the correct model increases. In addition, the coefficient estimates are closer to those of the true model. Forecast performance is one of the best in small samples, but approximately equal in large samples. Overall maenet performs well in high-dimensional small samples in terms of selecting the right variables and forecast performance. Empirical results also show a sparser model compared to the single-step adaptive elastic net methods. The gain in performance in especially small samples makes this model interesting for many fields, such as macroeconomics and finance.