# Statistical specification of jumps under semiparametric semimartingale models

Research output: Contribution to journalArticle

### Abstract

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 language English 209-227 19 Mathematical Methods of Statistics 17 3 https://doi.org/10.3103/S1066530708030034 Published - 2008 Sep Yes

### Fingerprint

Semimartingale
Jump
Specification
Estimating Function
Regression Function
Unknown Parameters
Model
Unknown
Estimate

### Keywords

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

### ASJC Scopus subject areas

• Statistics, Probability and Uncertainty
• Statistics and Probability

### Cite this

In: Mathematical Methods of Statistics, Vol. 17, No. 3, 09.2008, p. 209-227.

Research output: Contribution to journalArticle

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