Lasso VAR for VAR

White et al. (2015) extend the vector autoregressive (VAR) for conditional mean to VAR for conditional quantiles (VAR-VaR) to capture the interdependencies among the quantiles of multiple time series. In this paper, we introduce a post-lasso estimator to extend VAR-VaR to the high-dimensional case. As the structure of VAR-VaR makes it not easy to apply lasso directly, we propose to impose restrictions on parameters using a modified lasso quantile regression equation by equation. We then suggest a post-lasso estimator for VAR-VaR by pooling the restrictions for all equations. To solve the infeasibility caused by unobservable lagged quantiles, we propose an iteration procedure coupled with a quantile regression model selection criterion. Some Monte Carlo simulations and an empirical application show that our method produces better estimates for quantiles and quantile impulse response functions than the competing methods. Our method also has a significantly higher true discovery rate in simulations