Description

White et al. (2015) extend the vector autoregressive (VAR) for conditional mean to VAR for conditional quantiles (or Value at Risk, VaR), denoted as VAR for VaR (hereinafter VV), to capture the interdependencies among the quantiles of multiple time series. In this paper, we extend the VV model in two directions. First, we present a VAR for VaR model with asymmetric effects (VVA) that allows a negative shock to have a different impact on VaR than a positive shock. Second, we propose a post-lasso estimator LAVVA to solve the curse of dimensionality problem of VVA and VV. Some Monte Carlo simulations and an empirical application show that LAVVA produces better estimates for VaR and quantile impulse response functions (QIRF) than the competing methods. Some clear evidences of asymmetric effects on VaRs and QIRFs are also documented in the application.