Title: Confidence interval for correlation estimator between latent processes,
Abstract: Kimura and Yoshida treated a model in which the finite variation part of a
two-dimensional semimartingale is expressed by time-integration of latent
processes. They proposed a correlation estimator between the latent processes
and proved its consistency and asymptotic mixed normality. In this paper, we
discuss the confidence interval of the correlation estimator to detect the
correlation. %between latent processes. We propose two types of estimators for
asymptotic variance of the correlation estimator and prove their consistency in
a high frequency setting. Our model includes doubly stochastic Poisson
processes whose intensity processes are correlated Itô processes. We compare
our estimators based on the simulation of the doubly stochastic Poisson
processes.