Using Mixed-Frequency and Realized Measures in Quantile Regression

Abstract

Quantile regression is an efficient tool when it comes to estimate popular measures of tail risk such as the conditional quantile Value at Risk. In this paper we exploit the availability of data at mixed frequency to build a volatility model for daily returns with low-- (for macro--variables) and high--frequency (which may include an \virg{--X} term related to realized volatility measures) components. The quality of the suggested quantile regression model, labeled MF--Q--ARCH--X, is assessed in a number of directions: we derive weak stationarity properties, we investigate its finite sample properties by means of a Monte Carlo exercise and we apply it on financial real data. VaR forecast performances are evaluated by backtesting and Model Confidence Set inclusion among competitors, showing that the MF--Q--ARCH--X has a consistently accurate forecasting capability.