Before revision:  as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
After revision:  as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility to handle the microstructure noise of ultra high-frequency observations .