Ricerc@Sapienza

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 “–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

Forecasting conditional covariance matrices of returns involves a variety of modeling options. First, the choice between models based on daily or intradaily returns. Examples of the former are the Multivariate GARCH (MGARCH) models while models fitted to Realized Covariance (RC) matrices are examples of the latter. A second option, strictly related to the RC matrices, is given by the identification of the frequency at which the intradaily returns are observed. A third option concerns the proper estimation method able to guarantee unbiased parameter estimates even for large (MGARCH) models.