Estimation of integrated volatility of volatility with applications to goodness-of-fit testing
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Date
2011-12-06
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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.
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Keywords
central limit theorem, goodness-of-fit testing, high frequency observations, model validation, semimartingale, stable convergence, stochastic volatility model