Time-varying tail behavior for realized kernels

We propose a new score-driven model to capture the time-varying volatility and tail behavior of realized kernels. We assume realized kernels follow an F distribution with two time-varying degrees-of-freedom parameters, accounting for the Vol-of-Vol and the tail shape of the realized kernel distribution. The resulting score-driven dynamics imply that the influence of large (outlying) realized kernels on future volatilities and tail-shapes is mitigated. We apply our model to 30 stocks from the S&P 500 index over the period 2001-2014. The results show that tail shapes vary over time, even after correcting for the time-varying mean and Vol-of-Vol of the realized kernels. The model outperforms a number of recent competitors, both in-sample and out-of-sample. In particular, accounting for time-varying tail shapes matters for both density forecasts and forecasts of volatility risk quantiles.