Estimating functions for jump–diffusions

Research output: Contribution to journalJournal article – Annual report year: 2019Researchpeer-review

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Estimating functions for jump–diffusions. / Jakobsen, Nina Munkholt; Sørensen, Michael.

In: Stochastic Processes and their Applications, 2019.

Research output: Contribution to journalJournal article – Annual report year: 2019Researchpeer-review

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@article{2c6b655fb2844cc0a22a8fb65c9c5d2a,
title = "Estimating functions for jump–diffusions",
abstract = "Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate-optimality and efficiency are of particular concern. Under mild assumptions, it is shown that estimators of drift, diffusion, and jump parameters are consistent and asymptotically normal, as well as rate-optimal for the drift and jump parameters. Additional conditions are derived, which ensure rate-optimality for the diffusion parameter as well as efficiency for all parameters. The findings indicate a potentially fruitful direction for the further development of estimation for jump–diffusions.",
keywords = "Approximate martingale estimating function, Diffusion with jumps, Discrete-time sampling, Efficiency, Optimal rate, Stochastic differential equation",
author = "Jakobsen, {Nina Munkholt} and Michael S{\o}rensen",
year = "2019",
doi = "10.1016/j.spa.2018.09.006",
language = "English",
journal = "Stochastic Processes and Their Applications",
issn = "0304-4149",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Estimating functions for jump–diffusions

AU - Jakobsen, Nina Munkholt

AU - Sørensen, Michael

PY - 2019

Y1 - 2019

N2 - Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate-optimality and efficiency are of particular concern. Under mild assumptions, it is shown that estimators of drift, diffusion, and jump parameters are consistent and asymptotically normal, as well as rate-optimal for the drift and jump parameters. Additional conditions are derived, which ensure rate-optimality for the diffusion parameter as well as efficiency for all parameters. The findings indicate a potentially fruitful direction for the further development of estimation for jump–diffusions.

AB - Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate-optimality and efficiency are of particular concern. Under mild assumptions, it is shown that estimators of drift, diffusion, and jump parameters are consistent and asymptotically normal, as well as rate-optimal for the drift and jump parameters. Additional conditions are derived, which ensure rate-optimality for the diffusion parameter as well as efficiency for all parameters. The findings indicate a potentially fruitful direction for the further development of estimation for jump–diffusions.

KW - Approximate martingale estimating function

KW - Diffusion with jumps

KW - Discrete-time sampling

KW - Efficiency

KW - Optimal rate

KW - Stochastic differential equation

U2 - 10.1016/j.spa.2018.09.006

DO - 10.1016/j.spa.2018.09.006

M3 - Journal article

JO - Stochastic Processes and Their Applications

JF - Stochastic Processes and Their Applications

SN - 0304-4149

ER -