Mixed-frequency Quantile Regression Forests for Value-at-Risk forecasting

In this paper, we introduce Mixed-Frequency Quantile Regression Forests, a novel approach for non-parametrically computing conditional quantiles with mixed-frequency data to forecast the Value-at-Risk (VaR). By integrating the Mixed-Data Sampling (MIDAS) approach into Quantile Regression Forests (QRF), the proposed MIDAS-QRF specification incorporates information from both high and low frequencies, which would otherwise be unusable for VaR estimation in the context of random forests. Furthermore, leveraging the QRF approach allows us to capture non-linear relationships while accommodating skewed and fat-tailed distributions. We also propose a dynamic extension, MIDAS-DQRF, which introduces lagged VaR predictions as additional covariates. We extensively apply the MIDAS-QRF and MIDAS-DQRF specifications to forecast the VaR of energy futures, specifically WTI, Brent, and Heating Oil indices. By evaluating the proposed models through backtesting procedures, we provide empirical evidence of the validity of MIDAS-QRF and MIDAS-DQRF. Our findings indicate that these models generate statistically sound forecasts and generally outperform popular alternatives in terms of VaR forecast accuracy.