Do negative and positive equity returns share the same volatility dynamics?

This paper investigates whether positive and negative returns share the same dynamic volatility process. The well established stylized facts on volatility persistence and asymmetric effects are re-examined in light of such dichotomy. To analyze the dynamics of down and up volatilities estimated from daily re- turns I use a bivariate generalization of the standard EGARCH model. As a robustness check, I also investigate various specifications of down and up re- alized measures estimated from high-frequency data. The empirical findings point to the existence of a marked diversity in the volatilities of positive and negative daily returns in terms of persistence and sensitivity to good and bad news. A simple forecasting exercise highlights the striking performance of the proposed approach even in correspondence of the crisis period.