  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 It\^o processes. We compare
our estimators based on the simulation of the doubly stochastic Poisson
processes.
