Statistical specification of jumps under semiparametric semimartingale models. (English) Zbl 1231.62155
Summary: We consider a semimartingale with jumps that is driven by a finite activity Lévy process. Suppose that the Lévy measure is completely unknown, and that the jump component has a Markov structure depending on unknown parameters. This paper concentrates on estimating the parameters from continuous observations under a nonparametric setting of the Lévy measure. The estimating function is proposed by way of a nonparametric approach for some regression functions. At the end, we can specify jumps of the underlying Lévy process and estimate some Lévy characteristics jointly.
MSC:
| 62M09 | Non-Markovian processes: estimation |
| 62G08 | Nonparametric regression and quantile regression |
| 60G48 | Generalizations of martingales |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62M05 | Markov processes: estimation; hidden Markov models |
Keywords:
semimartingales with jumps; semiparametric model; regression estimation; consistency; specification of jumpsReferences:
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