B0627
Title: Parameter estimation for misspecified diffusion processes with noisy, nonsynchronous observations
Authors: Teppei Ogihara - University of Tokyo (Japan) [presenting]
Abstract: Forecasting variances of stocks and covariances of stock pairs is an important task to control the loss from stock assets for many financial institutions which hold a huge amount of stocks. The study of high-frequency data becomes more important because huge information of high-frequency data enable us to forecast stock variances and covariances more accurately. However, there are two problems with the statistical analysis of high-frequency data: market microstructure noise and nonsynchronous observations. We study parametric inference under the existence of market microstructure noise and nonsynchronous observations. We study maximum-likelihood-type estimation for parametric diffusion processes with noisy, nonsynchronous observations, assuming that the true model is contained in the parametric family. We further study the case that this assumption is not satisfied. Such a model is called a misspecified model. We will study the asymptotic theory of a maximum-likelihood-type estimator for misspecified models. 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.
