Volatility of Volatility and VIX Forecasting: New Evidence Based on Jumps, the Short‐Term and Long‐Term Volatility

ABSTRACT This study explores VIX forecasting by proposing a novel model to characterize the volatility of volatility based on high‐frequency VIX. Specifically, the decomposed jumps, the short‐ and long‐term volatility of VIX realized volatility obtained through wavelet analysis are considered by integrating the HAR‐DJI‐GARCH with GARCH‐MIDAS model. Empirical results show superior performance over competing models, with enhanced predictive accuracy under four non‐parametric jumps. The model's effectiveness is further validated by adjusting prediction windows, wavelet levels, examining VIX term structure, varying the significance level of jump test, and through the assessment of its economic significance.