Parametric estimation of Lévy processes

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6 Citations (Scopus)

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 languageEnglish
Pages (from-to)179-286
Number of pages108
JournalLecture Notes in Mathematics
Volume2128
DOIs
Publication statusPublished - Jan 1 2015

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Parametric Estimation
Stable Process
Estimating Function
Tail Probability
Method of Moments
Likelihood Function
Asymptotic Normality
Random Field
Likelihood
Jump
Rate of Convergence
Estimate
Model
Review
Class

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Parametric estimation of Lévy processes. / Masuda, Hiroki.

In: Lecture Notes in Mathematics, Vol. 2128, 01.01.2015, p. 179-286.

Research output: Contribution to journalArticle

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