Confidence interval for correlation estimator between latent processes

2017/10/18 by Kimura, Akitoshi
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1710.06683

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.

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