Smooth and Abrupt Dynamics in Financial Volatility: The MS‐MEM‐MIDAS*

Abstract

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.