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Parametric inference for nonsynchronously observed diffusion processes in the presence of market microstructure noise. (English) Zbl 1415.62064

Summary: 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 deterministic 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.

MSC:

62M05 Markov processes: estimation; hidden Markov models
60J60 Diffusion processes
62F12 Asymptotic properties of parametric estimators
62F15 Bayesian inference
62P20 Applications of statistics to economics
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