Two-step estimation of ergodic Lévy driven SDE

Hiroki Masuda, Yuma Uehara

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider high frequency samples from ergodic Lévy driven stochastic differential equation with drift coefficient a(x, α) and scale coefficient c(x, γ) involving unknown parameters α and γ. We suppose that the Lévy measure ν0, has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of α, γ and a class of functional parameter ∫ φ(z) ν0(dz) , which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of (α, γ) ; and then, for estimating ∫ φ(z) ν0(dz) we make use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator.

Original languageEnglish
Pages (from-to)105-137
Number of pages33
JournalStatistical Inference for Stochastic Processes
Volume20
Issue number1
DOIs
Publication statusPublished - Apr 1 2017

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Quasi-likelihood
Estimator
Method of Moments
Coefficient
Asymptotic Normality
Unknown Parameters
Stochastic Equations
Euler
Differential equation
Moment
Class

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Two-step estimation of ergodic Lévy driven SDE. / Masuda, Hiroki; Uehara, Yuma.

In: Statistical Inference for Stochastic Processes, Vol. 20, No. 1, 01.04.2017, p. 105-137.

Research output: Contribution to journalArticle

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