Confidence interval for correlation estimator between latent processes

TL;DR

This paper develops confidence intervals for correlation estimators between latent processes in semimartingale models, including doubly stochastic Poisson processes, and compares variance estimators through simulations.

Contribution

It introduces two consistent estimators for the asymptotic variance of the correlation estimator in high-frequency settings, extending previous work on correlation estimation.

Findings

Proposed two types of asymptotic variance estimators.

Proved consistency of the estimators.

Compared estimators via simulation of doubly stochastic Poisson 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.