Forecasting downside betas with multi-period components

Accurate forecasts of downside betas are critical for portfolio risk management because investors place greater weight on downside losses versus upside gains. While fractionally integrated models can capture persistence of downside betas, this approach solely utilizes information in samples related to downside market movements. We develop a Lasso HAR-type model that combines information from both downside and regular betas across multiple horizons. For downside betas measured over horizons exceeding three months, our proposed Lasso HAR-type model provides superior forecasting performance across both statistical and economic criteria. It consistently outperforms fractionally integrated models, effectively capturing the long-horizon dynamics of downside betas.