Moment inequalities for mixing long-span high-frequency data and strongly consistent estimation of OU integrated diffusion process Article Swipe

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Shanchao Yang , Jiaying Xie , Shuyi Luo , Zhiyong Li , Xin Yang ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1186/s13660-023-03065-2

Mixing is not much used in the high-frequency literature so far. However, mixing is a common weakly dependent property of continuous and discrete stochastic processes, such as Gaussian, Ornstein–Uhlenberck (OU), Vasicek, CIR, CKLS, logistic diffusion, generalized logistic diffusion, and double-well diffusion processes. So, long-span high-frequency data typically have weak dependence, and using mixing to study them is also an alternative approach. In this paper, we give some moment inequalities for long-span high-frequency data with ϕ -mixing, ρ -mixing, and α -mixing. These inequalities are effective tools for studying asymptotic properties. Applying these inequalities, we investigate the strong consistency of parameter estimation for the OU-integrated diffusion process. We also derive the mean square error of the estimation of the OU process and the optimal interval for the drift parameter estimator.

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Mixing (physics) Mathematics Estimator Moment (physics) Consistency (knowledge bases) Diffusion process Applied mathematics Diffusion Statistical physics Statistics Computer science Discrete mathematics Physics Quantum mechanics Knowledge management Innovation diffusion Classical mechanics Thermodynamics

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Type: article
Language: en
Landing Page: https://doi.org/10.1186/s13660-023-03065-2
PDF: https://journalofinequalitiesandapplications.springeropen.com/counter/pdf/10.1186/s13660-023-03065-2
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Cited By: 5
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DOI: https://doi.org/10.1186/s13660-023-03065-2

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Title: Moment inequalities for mixing long-span high-frequency data and strongly consistent estimation of OU integrated diffusion process

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Language: en

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Publication year: 2023

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Publication date: 2023-11-28

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Authors: Shanchao Yang, Jiaying Xie, Shuyi Luo, Zhiyong Li, Xin Yang

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Landing page: https://doi.org/10.1186/s13660-023-03065-2

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Concepts: Mixing (physics), Mathematics, Estimator, Moment (physics), Consistency (knowledge bases), Diffusion process, Applied mathematics, Diffusion, Statistical physics, Statistics, Computer science, Discrete mathematics, Physics, Quantum mechanics, Knowledge management, Innovation diffusion, Classical mechanics, Thermodynamics

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Cited by: 5

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publication_year	2023
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