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Title: Volatility of volatility: Estimation and tests based on noisy high frequency data Authors:  Yingying Li - Hong Kong University of Science and Technology (Hong Kong)
Guangying Liu - Nanjing Audit University (China)
Zhiyuan Zhang - Shanghai University of Finance and Economics (China) [presenting]
Abstract: A volatility of volatility estimator in a high frequency setting with noise and price jumps is proposed. We establish a feasible central limit theorem for the estimator that has a rate of convergence $n^{1/8}$. To our knowledge, this is the first instance where inference theories for volatility of volatility are obtained under this challenging setup. We further find that the rate of convergence can be improved to $n^{1/5}$ under the null that volatility processes are of bounded variation. This yields a test, which is more powerful than the one based on the general feasible central limit theorem, for the presence of diffusion components in volatility processes. Finite sample performance of the estimator and test statistic are examined by simulation studies. The empirical analysis shows that, for the stocks studied, volatility processes appear to have diffusion components.