Adding MIDAS terms to Linear ARCH models in a Quantile Regression framework

Recent financial crises have placed an increased accent on methods dealing with risk management. Despite some critiques, the Value-at-Risk (VaR) still plays today a leading role among the risk measures. For this reason, the financial econometrics literature has been involved in proposing as much as possible accurate VaR models. Recently, the quantile regression (QR) approach has been used to directly forecast the VaR measures. Within such a QR framework, we add a (MI(xed)- DA(ta) Sampling) term to the well known Linear ARCH (LARCH) model. The MIDAS term allows the inclusion of macroeconomic variables usually observed at low frequencies (monthly, quarterly, and so forth) in contexts where the dependent variable is generally observed at higher frequencies (mainly, daily). The resulting model, named Quantile LARCH-MIDAS (Q–LARCH–MIDAS), is the first model incorporating the MIDAS approach within the QR framework.