We design adaptive realized kernels to estimate the integrated volatility in a framework that combines a stochastic volatility model with leverage effect for the efficient price and a semiparametric microstructure noise model specied at the highest frequency. Some time dependence parameters of the noise model must be estimated before adaptive realized kernels can be implemented. We study their performance by simulation and illustrate their use with twelve stocks listed in the Dow Jones Industrial. As expected, we nd that adaptive realized kernels achieves the optimal trade-off between the discretization error and the microstructure noise.
