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. The aim of this paper is to investigate how the predictive accuracy of the HAR model depends on the choice of estimator, transformation, or combination scheme made by the market practitioner. In an out-of-sample study, covering the S&P 500 index and 26 frequently traded NYSE stocks, it is found that simple remedies systematically outperform not only standard HAR but also state of the art HARQ forecasts.

Keywords: Volatility forecasting, realized variance, HAR, HARQ, robust regression, weighted least squares, Box-Cox transformation, forecast comparisons, QLIKE, MSE, VaR, model confidence set

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