Forecasting Realized Volatility with Changing Average Levels

We explore the capability of regime switching with a Markovian dynamics (MS) and of a smooth transition (ST) nonlinearity within the class of Multiplicative Error Models (MEMs) to capture the slow moving long--run average in realized volatility. We compare these models to some alternatives, including the consideration of (quasi) long memory features (HAR class), the benefits of log transformations, and the presence of jumps. The analysis is applied to the realized kernel volatility series of the S\&P500 index, adopting residual diagnostics as a guidance to model selection. Forecast performance is evaluated and tested with squared and absolute losses both in-- and out--of--sample, as well as with a robustness check on different sample choices. The results show a very satisfactory performance of both MS and ST models, the former allowing also for the dating and the interpretation of regimes in terms of market events.