The Role of High-Frequency Prices, Long Memory and Jumps for Value-at-Risk Prediction

This study investigates the practical importance of several VaR modeling and forecasting issues in the context of intraday stock returns. Value-at-Risk (VaR) predictions obtained from daily GARCH models extended with additional information such as the realized volatility and squared overnight returns, are confronted with those from ARFIMA realized volatility models. The out-of-sample evaluation is based on a novel difference-in-proportions test that exploits the frequency of individual VaR rejections and a block-bootstrap unconditional coverage test that is robust to estimation uncertainty and model risk. ARFIMA models produce better backtesting results than GARCH models but fare worse in terms of independence of the hits sequence. Encompassing tests further suggest that GARCH and ARFIMA models can be fruitfully combined to produce more competitive VaR measures. We find evidence that intraday jumps also have forecasting potential. The techniques are illustrated for a small portfolio of large-cap stocks