Conditional Quantile Estimation for Linear ARCH Models with MIDAS Components

Recent financial crises have put an increased emphasis on methods devoted to risk management. Among a plethora of risk measures proposed in literature, the Value-at-Risk (VaR) plays still today a prominent role. Despite some criticisms, the VaR measures are fundamental in order to adequately set aside risk capital. For this reason, during the last decades the literature has been interested in proposing as much as possible accurate VaR models. Recently, the quantile regression approach has been used to directly forecast the VaR measures. We embed the linear AutoRegressive Conditional Heteroscedasticity (ARCH) model with MIDAS (MI(xed)-DA(ta) Sampling) term in such a quantile regression (QR) framework. The proposed model, named Quantile ARCH-MIDAS (Q–ARCH–MIDAS), allows to benefit from the information coming from variables observed at different frequencies with respect to that of the variable of interest. Moreover, the QR context brings additional advantages, such as the robustness to the presence of outliers and the lack of distributional assumptions.