Estimating functions for jump–diffusions

Nina Munkholt Jakobsen; Michael Sørensen

doi:10.1016/j.spa.2018.09.006

Estimating functions for jump–diffusions

Nina Munkholt Jakobsen^*, Michael Sørensen

^*Corresponding author for this work

Department of Mathematical Sciences

2 Citations (Scopus)

10 Downloads (Pure)

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.

Original language	English
Journal	Stochastic Processes and Their Applications
Volume	129
Pages (from-to)	3282–3318
ISSN	0304-4149
DOIs	https://doi.org/10.1016/j.spa.2018.09.006
Publication status	Published - Sept 2019

Keywords

Approximate martingale estimating function
Diffusion with jumps
Discrete-time sampling
Efficiency
Optimal rate
Stochastic differential equation

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10.1016/j.spa.2018.09.006

MunkholtSørensenAccepted author manuscript, 785 KBLicence: CC BY-NC-ND

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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.",

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TY - JOUR

T1 - Estimating functions for jump–diffusions

AU - Jakobsen, Nina Munkholt

AU - Sørensen, Michael

PY - 2019/9

Y1 - 2019/9

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

UR - http://www.scopus.com/inward/record.url?scp=85054083179&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2018.09.006

DO - 10.1016/j.spa.2018.09.006

M3 - Journal article

AN - SCOPUS:85054083179

SN - 0304-4149

VL - 129

SP - 3282

EP - 3318

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Estimating functions for jump–diffusions

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