Exponential high-frequency-based-volatility (EHEAVY) models

This paper proposes an Exponential HEAVY (EHEAVY) model. The model specifies the dynamics of returns and realized measures of volatility in an exponential form, which guarantees the positivity of volatility without restrictions on parameters and naturally allows the asymmetric effects. It provides a more flexible modelling of the volatility than the HEAVY models. A joint quasi-maximum likelihood estimation and closed form multi-step ahead forecasting is derived. The model is applied to 31 assets extracted from the Oxford-Man Institute's realized library. The empirical results show that the dynamic of return volatility is driven by the realized measure, while the asymmetric effect is captured by the return shock (not by the realized return shock). Hence, both return and realized measure are included in the return volatility equation. Out-of-sample forecast and portfolio exercise further shows the superior forecasting performance of the EHEAVY model, in both statistical and economic sense.