  We study parametric inference for diffusion processes when observations occur
nonsynchronously and are contaminated by market microstructure noise. We
construct a quasi-likelihood function and study asymptotic mixed normality of
maximum-likelihood- and Bayes-type estimators based on it. We also prove the
local asymptotic normality of the model and asymptotic efficiency of our
estimator when the diffusion coefficients are constant and noise follows a
normal distribution. We conjecture that our estimator is asymptotically
efficient even when the latent process is a general diffusion process. An
estimator for the quadratic covariation of the latent process is also
constructed. Some numerical examples show that this estimator performs better
compared to existing estimators of the quadratic covariation.
