TY - JOUR
T1 - Two-step estimation of ergodic Lévy driven SDE
AU - Masuda, Hiroki
AU - Uehara, Yuma
N1 - Funding Information:
We are grateful to the referees for careful reading and constructive comments, which led to substantial improvements of the earlier version of this paper. This work was partly supported by JSPS KAKENHI Grant Numbers 26400204 (H. Masuda) and JST, CREST.
Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s11203-016-9133-5
DO - 10.1007/s11203-016-9133-5
M3 - Article
AN - SCOPUS:84957624600
SN - 1387-0874
VL - 20
SP - 105
EP - 137
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
IS - 1
ER -