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Title: Parameter estimation for misspecified diffusion with market microstructure noise Authors:  Teppei Ogihara - University of Tokyo (Japan) [presenting]
Abstract: Statistical inference for stock prices modeled by diffusion processes with high-frequency observations is considered. In particular, we study parametric inference under the existence of market microstructure noise and nonsynchronous observations. We first consider maximum-likelihood-type estimation for parametric diffusion processes with noisy, nonsynchronous observations, assuming that the true model is contained in the parametric family. We show asymptotic mixed normality of the estimator with the convergence rate $n^{-1/4}$. We also see local asymptotic normality of the statistical model when coefficients of the stochastic differential equation are deterministic,and show asymptotic efficiency of the estimator. In practice for high-frequency financial data, it is not easy task to choose parametric family so that the true model is contained in the parametric family. The statistical model without this assumption is called `misspecified model'. In this setting, the maximum-likelihood-type estimator cannot attain the optimal convergence rate $n^{-1/4}$ due to the asymptotic bias. We construct a new estimator which attains the optimal rate by using a bias correction and show the asymptotic mixed normality.