Multiple-step value-at-risk forecasts based on volatility-filtered MIDAS quantile regression: Evidence from major investment assets


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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.

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.

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    • Figure 1. Out-of-sample forecasts of the 5-step and 10-step VaR for the FTSE100 index at the 2.5% risk level
    • Table 1. Summary of testing results for the out-of-sample 5-step and 10-step VaR forecasts
    • Table A1. Descriptive statistics of daily, 5-day, and 10-day returns
    • Table A2. Estimation of the GARCH(1,1)-t components in the F-MIDAS-Q model
    • Table A3. Parameter estimation of F-MIDAS-Q model under the 5-step holding period
    • Table A4. Parameter estimation of F-MIDAS-Q model under the 10-step holding period
    • Conceptualization
      Qian Chen, Xiaoxuan Huang
    • Investigation
      Qian Chen, Xiang Gao, Xi Li
    • Methodology
      Qian Chen, Xiang Gao, Xi Li
    • Project administration
      Qian Chen
    • Validation
      Qian Chen, Xiang Gao, Xiaoxuan Huang, Xi Li
    • Supervision
      Xiang Gao, Xi Li
    • Writing – review & editing
      Xiang Gao, Xi Li
    • Data curation
      Xiaoxuan Huang
    • Formal Analysis
      Xiaoxuan Huang
    • Visualization
      Xiaoxuan Huang
    • Writing – original draft
      Xiaoxuan Huang