The Heterogeneous Autoregressive (HAR) model of Corsi (2009) has become the benchmark model for predicting realized volatility given its simplicity and consistent empirical performance. Many modifications and extensions to the original model have been proposed that often only provide incremental...

This paper demonstrates that existing quantile regression models used for forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. A Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as...

This paper proposes two new approaches to improve estimation of the coefficients of the multivariate HAR (MHAR) model, and in turn improve forecast performance. A robust estimator of the covariance matrix is adopted to replace the realized covariance (RCov) matrix while estimating the MHAR...