In the financial econometrics literature, the use of quantile regression to estimate risk measures, such as the Value-at-Risk (VaR), has enormously increased in the last years. The goal of this research proposal is twofold. First, we aim at including in the quantile regression model variables observed at different frequencies than the dependent one by introducing a MI(xed)-DA(ta) Sampling terms in the AutoRegressive Conditional Heteroskedasticity (ARCH) model, estimated using quantile regressions. The MIDAS term allows in fact for the inclusion of variables usually observed at lower frequencies than the dependent variable. This mixing frequency approach can accommodate contexts where the dependent variable is observed daily and some covariates are observed at lower frequencies which is quite common in financial framework where macroeconomic variables are usually observed at monthly or quarterly frequencies and considered as driving forces of the assets' volatility. Therefore, the inclusion of such information may largely improve the estimation of the risk measures of interest in particular the VaR calculated using quantile regression approach. The estimation of the VaR measures through the quantile regression tools may benefit of many advantages. The proposed model, named Q-ARCH-MIDAS, will be extensively evaluated from the statistical point of view and in a large empirical application. The second aim of the present research proposal deals with the choice of the best model to forecast the VaR. The problem of ranking and evaluating several models is largely recognized in the financial econometrics literature. In this context, we aim at introducing the Partially Ordered SETs (POSETs) to analyze different risk models (among which there is also the proposed Q-ARCH-MIDAS). The POSET-based approach uses different loss functions characterized by peculiar aspects to rank the models controlling their degree of incomparability.
