Smooth and Abrupt Dynamics in Financial Volatility: the MS-MEM-MIDAS

In this paper, we maintain that the evolution of the realized volatility is characterized by a combination of high-frequency dynamics and smoother, yet persistent, dynamics evolving at a lower frequency. We suggest a new Multiplicative Error Model which combines the mixed frequency features of a MIDAS at the monthly level with Markovian dynamics at the daily level. When estimated in-sample on the realized kernel volatility of the S&P500 index, this model dominates other simpler specifications, especially when monthly aggregated realized volatility is used. The same pattern is confirmed in the out-of-sample forecasting performance which suggests that adding an abrupt change in the average level of volatility better helps in tracking quick bursts of volatility and a relatively rapid absorption of the shocks.