Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts
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We study the asymptotic normality of two estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate n^1/4, while the estimator without bias-correction has a slower convergence rate and a smaller asymptotic variance. Additionally, we provide simulation results that support the theoretical asymptotic distribution of the rate-efficient estimator and show the accuracy of the Fourier estimator in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, we reconstruct the daily volatility of volatility of the S P500 and EUROSTOXX50 indices over long samples via the rate-optimal Fourier estimator and provide novel insight into the existence of stylized facts about its dynamics.
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