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Confidence interval for correlation estimator between latent processes

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Abstract

Kimura and Yoshida (Estimation of correlation between latent processes. Springer International Publishing, Cham. pp 131–146, 2016) 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. 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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Acknowledgements

The author thanks two referees of this journal for their detailed comments to the earlier version of this paper. The author also thanks his supervisor Prof. Nakahiro Yoshida who provided valuable suggestions and comments.

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Authors and Affiliations

  1. Faculty of Science and Engineering Waseda University, Center for Science and Engineering, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Akitoshi Kimura

  2. Japan Science and Technology Agency, CREST, Kawaguchi, Japan

    Akitoshi Kimura

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  1. Akitoshi Kimura
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Correspondence to Akitoshi Kimura.

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Kimura, A. Confidence interval for correlation estimator between latent processes. Jpn J Stat Data Sci 2, 323–346 (2019). https://doi.org/10.1007/s42081-019-00036-0

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