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 It\^o processes. We compare our estimators based on the simulation of the doubly stochastic Poisson processes.
Cite
@article{arxiv.1710.06683,
title = {Confidence interval for correlation estimator between latent processes},
author = {Akitoshi Kimura},
journal= {arXiv preprint arXiv:1710.06683},
year = {2018}
}