Forecasting realized volatility using HAR models and wavelet decomposition: A volatility-timing perspective

• HAR models are used to forecast Realized Volatility (RV) for a portfolio of stocks. • Low-, medium-, and high-frequency components of RV are isolated using wavelet decomposition. • Low-frequency volatility forecasts improve utility and reduce portfolio turnover. • Benefits are robust to direct forecasts of portfolio weights and jump robust RV. • Results stress the distinction between statistical and practical performance metrics in volatility forecasting. This study proposes a wavelet-based approach to forecasting Realized Volatility (RV) and evaluates its economic value within a volatility-timing framework. We apply wavelet decomposition to separate short-, medium-, and long-term components and generate forecasts using Heterogeneous Autoregressive (HAR) models. Forecasts based on the low-frequency component consistently lead to better portfolio outcomes, reducing turnover and enhancing investor utility without increasing risk. These results hold even when portfolio weights are forecast directly after being constructed from RV, or when jump-robust volatility estimates are used. The results highlight the importance of aligning forecast evaluation with practical investment objectives. Forecasts delivering the greatest welfare gains may not minimize conventional statistical loss functions.