## Bernoulli

• Bernoulli
• Volume 21, Number 4 (2015), 2393-2418.

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

Mathias Vetter

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 21, Number 4 (2015), 2393-2418.

Dates
Revised: March 2014
First available in Project Euclid: 5 August 2015

https://projecteuclid.org/euclid.bj/1438777598

Digital Object Identifier
doi:10.3150/14-BEJ648

Mathematical Reviews number (MathSciNet)
MR3378471

Zentralblatt MATH identifier
1125.62084

#### Citation

Vetter, Mathias. Estimation of integrated volatility of volatility with applications to goodness-of-fit testing. Bernoulli 21 (2015), no. 4, 2393--2418. doi:10.3150/14-BEJ648. https://projecteuclid.org/euclid.bj/1438777598

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#### Supplemental materials

• Additional proofs for claims made in the article. We provide several proofs for either theorems from the main corpus or additional steps discussed in the \hyperref[app]Appendix.