Statistical specification of jumps under semiparametric semimartingale models

Ya Shimizu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider a semimartingale with jumps that are driven by a finite activity Lévy process. Suppose that the Lévy measure is completely unknown, and that the jump component has a Markovian structure depending on unknown parameters. This paper concentrates on estimating the parameters from continuous observations under the nonparametric setting on the Lévy measure. The estimating function is proposed by way of nonparametric approach for some regression functions. In the end, we can specify jumps of the underlying Lévy process and estimate some Lévy characteristics jointly.

Original languageEnglish
Pages (from-to)209-227
Number of pages19
JournalMathematical Methods of Statistics
Issue number3
Publication statusPublished - 2008 Sept
Externally publishedYes


  • consistency
  • regression estimation
  • semimartingales with jumps
  • semiparametric model
  • specification of jumps

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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