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Estimating functions for jump–diffusions

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  • Jakobsen, Nina Munkholt
  • Sørensen, Michael

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.

Suggested Citation

  • Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3282-3318
    DOI: 10.1016/j.spa.2018.09.006
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    References listed on IDEAS

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