Prediction-based estimation for diffusion models with high-frequency data

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Prediction-based estimation for diffusion models with high-frequency data. / Jorgensen, Emil S.; Sorensen, Michael.

I: Japanese Journal of Statistics and Data Science, Bind 4, Nr. 1, 2021, s. 483-511.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Jorgensen, ES & Sorensen, M 2021, 'Prediction-based estimation for diffusion models with high-frequency data', Japanese Journal of Statistics and Data Science, bind 4, nr. 1, s. 483-511. https://doi.org/10.1007/s42081-020-00103-x

APA

Jorgensen, E. S., & Sorensen, M. (2021). Prediction-based estimation for diffusion models with high-frequency data. Japanese Journal of Statistics and Data Science, 4(1), 483-511. https://doi.org/10.1007/s42081-020-00103-x

Vancouver

Jorgensen ES, Sorensen M. Prediction-based estimation for diffusion models with high-frequency data. Japanese Journal of Statistics and Data Science. 2021;4(1):483-511. https://doi.org/10.1007/s42081-020-00103-x

Author

Jorgensen, Emil S. ; Sorensen, Michael. / Prediction-based estimation for diffusion models with high-frequency data. I: Japanese Journal of Statistics and Data Science. 2021 ; Bind 4, Nr. 1. s. 483-511.

Bibtex

@article{b2c1ea379fd14d8092284d15abbab805,
title = "Prediction-based estimation for diffusion models with high-frequency data",
abstract = "This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high-frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are observations of a diffusion process at n equidistant time points Δni, and the asymptotic scenario is Δn→0 and nΔn→∞. For useful and tractable classes of prediction-based estimating functions, existence of a consistent estimator is proved under standard weak regularity conditions on the diffusion process and the estimating function. Asymptotic normality of the estimator is established under the additional rate condition nΔ3n→0. The prediction-based estimating functions are approximate martingale estimating functions to a smaller order than what has previously been studied, and new non-standard asymptotic theory is needed. A Monte Carlo method for calculating the asymptotic variance of the estimators is proposed.",
keywords = "Diffusion process, High-frequency data, Infinitesimal generator, Potential operator, Parametric inference, Prediction-based estimating function, <mml, math><mml, mi>rho</mml, mi></mml, math>, documentclass[12pt]{minimal}, usepackage{amsmath}, usepackage{wasysym}, usepackage{amsfonts}, usepackage{amssymb}, usepackage{amsbsy}, usepackage{mathrsfs}, usepackage{upgreek}, setlength{, oddsidemargin}{-69pt}, begin{document}$$, rho$$, end{document}<inline-graphic xlink, href={"}42081_2020_103_Article_IEq5, gif{"}, >-mixing",
author = "Jorgensen, {Emil S.} and Michael Sorensen",
year = "2021",
doi = "10.1007/s42081-020-00103-x",
language = "English",
volume = "4",
pages = "483--511",
journal = "Japanese Journal of Statistics and Data Science",
issn = "2520-8764",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Prediction-based estimation for diffusion models with high-frequency data

AU - Jorgensen, Emil S.

AU - Sorensen, Michael

PY - 2021

Y1 - 2021

N2 - This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high-frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are observations of a diffusion process at n equidistant time points Δni, and the asymptotic scenario is Δn→0 and nΔn→∞. For useful and tractable classes of prediction-based estimating functions, existence of a consistent estimator is proved under standard weak regularity conditions on the diffusion process and the estimating function. Asymptotic normality of the estimator is established under the additional rate condition nΔ3n→0. The prediction-based estimating functions are approximate martingale estimating functions to a smaller order than what has previously been studied, and new non-standard asymptotic theory is needed. A Monte Carlo method for calculating the asymptotic variance of the estimators is proposed.

AB - This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high-frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are observations of a diffusion process at n equidistant time points Δni, and the asymptotic scenario is Δn→0 and nΔn→∞. For useful and tractable classes of prediction-based estimating functions, existence of a consistent estimator is proved under standard weak regularity conditions on the diffusion process and the estimating function. Asymptotic normality of the estimator is established under the additional rate condition nΔ3n→0. The prediction-based estimating functions are approximate martingale estimating functions to a smaller order than what has previously been studied, and new non-standard asymptotic theory is needed. A Monte Carlo method for calculating the asymptotic variance of the estimators is proposed.

KW - Diffusion process

KW - High-frequency data

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U2 - 10.1007/s42081-020-00103-x

DO - 10.1007/s42081-020-00103-x

M3 - Journal article

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EP - 511

JO - Japanese Journal of Statistics and Data Science

JF - Japanese Journal of Statistics and Data Science

SN - 2520-8764

IS - 1

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ID: 284424818