Estimation of integrated volatility of volatility with applications to goodness-of-fit testing

Abstract

In this paper we are concerned with non-parametric inference on the volatility of volatility process r2 in stochastic volatility models. We construct an estimator for its integrated version R t 0 2 s ds in a high frequency setting which is based on increments of spot volatility estimators, and we are able to prove both feasible and infeasible central limit theorems at the optimal rate n-1/4. Such CLTs 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 apply our results to goodness-of- fit testing, providing the first consistent test for a certain parametric form of the volatility of volatility.