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Consistency and asymptotics of a Poisson intensity least-squares estimator for partially observed jump–diffusion processes

Author

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  • Djouadi, Seddik M.
  • Maroulas, Vasileios
  • Pan, Xiaoyang
  • Xiong, Jie

Abstract

A least-squares estimator of the intensity of a Poisson process is studied for a partially observed stochastic system, where the signal evolves as a jump–diffusion process and the observation is a diffusion process. Precisely, we establish the consistency and a central limit theorem of the least-squares estimator when a negative drift coefficient for the jump–diffusion process is considered. We also demonstrate that the variance and the fourth moment of the estimator are bounded but inconsistent when the drift coefficient of the jump diffusion is positive or data is collected within a fixed time horizon.

Suggested Citation

  • Djouadi, Seddik M. & Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2017. "Consistency and asymptotics of a Poisson intensity least-squares estimator for partially observed jump–diffusion processes," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 8-16.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:8-16
    DOI: 10.1016/j.spl.2016.11.017
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    References listed on IDEAS

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    1. Michael Rockinger & Maria Semenova, 2005. "Estimation of Jump-Diffusion Process vis Empirical Characteristic Function," FAME Research Paper Series rp150, International Center for Financial Asset Management and Engineering.
    2. Maroulas, Vasileios & Xiong, Jie, 2013. "Large deviations for optimal filtering with fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2340-2352.
    3. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
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