A Generalized Heterogeneous Autoregressive Model using the Market Index

This paper shows that generalizing the heterogeneous autoregressive model (HAR) with realized (co)variances and semi-(co)variances from the index leads to more accurate volatility forecasts. To circumvent the effects of the market microstructure noise arising from using high sampling frequencies, we adopt noise-robust estimators for the realized (co)variances and develop novel noise-robust estimators for the semi-(co)variances. To explore the sampling frequency at which the forecasting gains are maximized, we adopt a mixed-sampling approach that iterates over several sampling frequencies of the stock and the index. Our analysis shows that gains are maximized at the combination of a low (high) frequency on the stock (index). We illustrate that the observed forecasting gains translates into economic gains such that a risk-averse investor is willing to pay up to 57 annual basis points by adopting a model specification that utilizes the index information.