Enhancing Volatility Prediction: A Wavelet‐Based Hierarchical Forecast Reconciliation Approach

Abstract

Forecasting realized volatility (RV) has been widely studied, with numerous techniques developed to enhance predictive accuracy. Among these techniques, the use of RV decompositions based on intraday asset returns has been applied. However, the use of a frequency‐based decomposition, which provides unique insights into the dynamics of RV, remains relatively unexplored. This study develops a novel frequency‐based (wavelet decomposition) hierarchical forecast reconciliation approach for RV forecasting. Our proposed approach relies on decomposing RV into low, medium, and high frequency components, forecasting these sub‐series individually via the HAR model, and applying forecast reconciliation to produce the final RV prediction. Empirical results demonstrate that our proposed wavelet‐based framework achieves superior predictive and economically significant performance relative to models employing return‐based decompositions and the benchmark HAR, and logarithmic HAR models. The findings also reveal that the wavelet approach provides greater gains at longer forecast horizons, owing to the strong persistence in the low‐frequency component of RV. Moreover, this wavelet approach performs well in periods of high volatility and across all market conditions through time.