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 language | English |
|---|---|
| Pages (from-to) | 105-137 |
| Number of pages | 33 |
| Journal | Statistical Inference for Stochastic Processes |
| Volume | 20 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Apr 1 2017 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
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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 journal › Article
}
TY - JOUR
T1 - Two-step estimation of ergodic Lévy driven SDE
AU - Masuda, Hiroki
AU - Uehara, Yuma
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.
UR - http://www.scopus.com/inward/record.url?scp=84957624600&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84957624600&partnerID=8YFLogxK
U2 - 10.1007/s11203-016-9133-5
DO - 10.1007/s11203-016-9133-5
M3 - Article
AN - SCOPUS:84957624600
VL - 20
SP - 105
EP - 137
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
SN - 1387-0874
IS - 1
ER -