Mixed-frequency quantile regression with realized volatility to forecast Value-at-Risk

Abstract

The use of quantile regression to calculate risk measures has been widely recognized in the financial econometrics literature. When data are observed at mixed-frequency, the standard quantile regression models are no longer adequate. In this paper, we develop a model built on a mixed-frequency quantile regression to directly estimate the Value-at-Risk. In particular, the low-frequency component incorporates information coming from variables observed at, typically, monthly or lower frequencies, while the high-frequency component can include a variety of daily variables, like realized volatility measures or market indices. We derive the conditions for the weak stationarity of the daily return process suggested while the finite sample properties are investigated in an extensive Monte Carlo exercise. The validity of the proposed model is then explored through a real data application using the most important financial indexes. We show that our model outperforms other competing specifications, using backtesting and Model Confidence Set procedures

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