Xiang Gao

Forecasting multiple-step value-at-risk (VaR) consistently across asset classes is hindered by the limited sample size of low-frequency returns and the potential model misspecification when assuming identical return distributions over different holding periods. This paper hence investigates the predictive power for multi-step VaR of a framework that models separately the volatility component and the error term of the return distribution. The proposed model is illustrated with ten asset returns series including global stock markets, commodity futures, and currency exchange products. The estimation results confirm that the volatility-filter residuals demonstrate distinguished tail dynamics to that of the return series. The estimation results suggest that volatility-filtered residuals may have either negative or positive tail dependence, unlike the unanimous negative tail dependence in the return series. By comparing the proposed model to several alternative approaches, the results from both the formal and informal tests show that the specification under concern performs equivalently well if not better than its top competitors at the 2.5% and 5% risk level in terms of accuracy and validity. The proposed model also generates more consistent VaR forecasts under both the 5-step and 10-step setup than the MIDAS-Q model.

Acknowledgment
The authors are grateful to the editor and an anonymous referee. This research is sponsored by the National Natural Science Foundation of China (Award Number: 71501117). All remaining errors are our own.