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 tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
KW - Infinitesimal generator
KW - Potential operator
KW - Parametric inference
KW - Prediction-based estimating function
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U2 - 10.1007/s42081-020-00103-x
DO - 10.1007/s42081-020-00103-x
M3 - Journal article
VL - 4
SP - 483
EP - 511
JO - Japanese Journal of Statistics and Data Science
JF - Japanese Journal of Statistics and Data Science
SN - 2520-8764
IS - 1
ER -
ID: 284424818