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We propose a novel class of volatility estimators named the renewal based volatility estimators for high-frequency volatility estimation, which is constructed based on a renewal process in business time. We show the consistency and derive the asymptotic distribution of this class of estimators, and show that a parametric structure can lead to significant gains in the efficiency of volatility estimation compared to a pure non-parametric design. This class of estimators includes all the parametric and non-parametric estimators that are based on an absolute price change point process, e.g. Engle and Russell (1998), Gerhard and Hautsch (2002), Tse and Yang (2012) and Nolte, Taylor, and Zhao (2016). We examine the nonparametric duration (NPD) based volatility estimator proposed by Nolte, Taylor, and Zhao (2016), and show the properties of this estimator in the presence of drift, jump, time discretization, a general market microstructure (MMS) noise and price discretization noise. The main finding is that the NPD estimator is very robust to the presence of jumps but is generally biased due to time discretization and the MMS noise. Through simulations we show that the NPD estimator is more efficient than calendar time sampled RV-type estimators in the absence of MMS noise, but also that it is much more sensitive to the MMS noise than calendar time sampling methods. We propose an exponentially smoothed NPD estimator and show that it can signicantly outperform commonly used calendar time bias corrected volatility estimators in terms of efficiency. Additionally, we propose a range-duration based renewal type volatility estimator that can outperform a general realized variance (RV) estimator under any sampling scheme.
