  In this paper, we are concerned with nonparametric inference on the
volatility of volatility process in stochastic volatility models. We construct
several estimators for its integrated version in a high-frequency setting, all
based on increments of spot volatility estimators. Some of those are positive
by construction, others are bias corrected in order to attain the optimal rate
$n^{-1/4}$. Associated central limit theorems are proven which can be widely
used in practice, as they are the key to essentially all tools in model
validation for stochastic volatility models. As an illustration we give a brief
idea on a goodness-of-fit test in order to check for a certain parametric form
of volatility of volatility.
