Discrete-time volatility forecasting: A quantile regression approach

Abstract

We propose the Heterogeneous Quantile Autoregressive Distributed Lag Realized Volatility, with Jumps and Leverage Effect (HQADL-RV-JL) model. The specification is nested in the HAR class under the Autoregressive Distributed Lag quantile regression framework. The model was estimated on an equispaced grid ranging from 0.01 to 0.99, spanning 99 quantile levels, using the S&P 500 index high-frequency returns. In-sample results suggest that the semiparametric specification is able to capture the main stylized facts of volatility for a high-frequency return series. Out-of-sample performance shows that the median forecast of our model is as good as forecasting the conditional expectation of Corsi and Renò (2012) in the medium and long term. Moreover, we provide an original contribution by forecasting the conditional probability density of the Realized Volatility, yielding a predicted volatility density one step ahead.