Estimating functions for jump–diffusions
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Estimating functions for jump–diffusions. / Jakobsen, Nina Munkholt; Sørensen, Michael.
In: Stochastic Processes and Their Applications, Vol. 129, 2019, p. 3282–3318.Research output: Contribution to journal › Journal article › Research › peer-review
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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
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
VL - 129
SP - 3282
EP - 3318
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
ER -
ID: 203665203