A Practical Guide to Harnessing the HAR Volatility Model

Abstract

The standard heterogeneous autoregressive (HAR) model is perhaps the most popular benchmark model for forecasting return volatility. It is often estimated using raw realized variance (RV) and ordinary least squares (OLS). However, given the stylized facts of RV and well-known properties of OLS, this combination should be far from ideal. One goal of this paper is to investigate how the predictive accuracy of the HAR model depends on the choice of estimator, transformation, and forecasting scheme made by the market practitioner. Another goal is to examine the effect of replacing its high-frequency data based volatility proxy (RV) with a proxy based on free and publicly available low-frequency data (logarithmic range). In an out-of-sample study, covering three major stock market indices over 16 years, it is found that simple remedies systematically outperform not only standard HAR but also state of the art HARQ forecasts, and that HAR models using logarithmic range can often produce forecasts of similar quality to those based on RV.

Keywords: Volatility forecasting, realized variance, HAR model, HARQ model, robust regression, Box-Cox transformation, forecast comparisons, QLIKE loss, model confidence set

JEL Classification: C22, C51, C52, C53, C58