Evaluating Forecast Distributions in Neural Network HAR-Type Models for Range-Based Volatility

In this paper, we focus on a range-based measure for volatility and present a forecasting tool combining the heterogeneous autoregressive model with feed-forward neural networks. Using a bootstrap scheme, we can also obtain the forecast distributions, which are useful to evaluate how much uncertainty is associated with each point forecast. An application to real data shows a significant contribution of the proposed methodology to improving forecast accuracy in terms of point forecasts and forecast distributions.