  Data observed at high sampling frequency are typically assumed to be an
additive composite of a relatively slow-varying continuous-time component, a
latent stochastic process or a smooth random function, and measurement error.
Supposing that the latent component is an It\^{o} diffusion process, we propose
to estimate the measurement error density function by applying a deconvolution
technique with appropriate localization. Our estimator, which does not require
equally-spaced observed times, is consistent and minimax rate optimal. We also
investigate estimators of the moments of the error distribution and their
properties, propose a frequency domain estimator for the integrated volatility
of the underlying stochastic process, and show that it achieves the optimal
convergence rate. Simulations and a real data analysis validate our analysis.
