### Abstract

The main purpose of this chapter is to present some theoretical aspects of parametric estimation of Lévy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of explicit estimating functions are discussed. In addition to the asymptotic normality at several rates of convergence, a uniform tail-probability estimate for statistical random fields is given. As specific cases, we discuss method of moments for the stable Lévy processes in much greater detail, with briefly mentioning locally stable Lévy processes too. Also discussed is, due to its theoretical importance, a brief review of how the classical likelihood approach works or does not, beyond the fact that the likelihood function is not explicit.

Original language | English |
---|---|

Pages (from-to) | 179-286 |

Number of pages | 108 |

Journal | Lecture Notes in Mathematics |

Volume | 2128 |

DOIs | |

Publication status | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

**Parametric estimation of Lévy processes.** / Masuda, Hiroki.

Research output: Contribution to journal › Article

*Lecture Notes in Mathematics*, vol. 2128, pp. 179-286. https://doi.org/10.1007/978-3-319-12373-8_3

}

TY - JOUR

T1 - Parametric estimation of Lévy processes

AU - Masuda, Hiroki

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The main purpose of this chapter is to present some theoretical aspects of parametric estimation of Lévy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of explicit estimating functions are discussed. In addition to the asymptotic normality at several rates of convergence, a uniform tail-probability estimate for statistical random fields is given. As specific cases, we discuss method of moments for the stable Lévy processes in much greater detail, with briefly mentioning locally stable Lévy processes too. Also discussed is, due to its theoretical importance, a brief review of how the classical likelihood approach works or does not, beyond the fact that the likelihood function is not explicit.

AB - The main purpose of this chapter is to present some theoretical aspects of parametric estimation of Lévy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of explicit estimating functions are discussed. In addition to the asymptotic normality at several rates of convergence, a uniform tail-probability estimate for statistical random fields is given. As specific cases, we discuss method of moments for the stable Lévy processes in much greater detail, with briefly mentioning locally stable Lévy processes too. Also discussed is, due to its theoretical importance, a brief review of how the classical likelihood approach works or does not, beyond the fact that the likelihood function is not explicit.

UR - http://www.scopus.com/inward/record.url?scp=84917708888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84917708888&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-12373-8_3

DO - 10.1007/978-3-319-12373-8_3

M3 - Article

AN - SCOPUS:84917708888

VL - 2128

SP - 179

EP - 286

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

SN - 0075-8434

ER -