Abstract
We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations. We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process with a Lévy measure f θ(z)dz, and we admit the case f θ(z)dz=∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation results for some simple models.
| Original language | English |
|---|---|
| Pages (from-to) | 179-225 |
| Number of pages | 47 |
| Journal | Statistical Inference for Stochastic Processes |
| Volume | 9 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2006 Jul |
| Externally published | Yes |
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Keywords
- Asymptotic normality
- Diffusion process with jumps
- Discrete observation
- Infinitely many jumps
- M-estimation
- Parametric inference
- Partial efficiency
ASJC Scopus subject areas
- Mathematics(all)
Cite this
M-estimation for discretely observed ergodic diffusion processes with infinitely many jumps. / Shimizu, Yasutaka.
In: Statistical Inference for Stochastic Processes, Vol. 9, No. 2, 07.2006, p. 179-225.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - M-estimation for discretely observed ergodic diffusion processes with infinitely many jumps
AU - Shimizu, Yasutaka
PY - 2006/7
Y1 - 2006/7
N2 - We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations. We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process with a Lévy measure f θ(z)dz, and we admit the case f θ(z)dz=∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation results for some simple models.
AB - We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations. We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process with a Lévy measure f θ(z)dz, and we admit the case f θ(z)dz=∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation results for some simple models.
KW - Asymptotic normality
KW - Diffusion process with jumps
KW - Discrete observation
KW - Infinitely many jumps
KW - M-estimation
KW - Parametric inference
KW - Partial efficiency
UR - http://www.scopus.com/inward/record.url?scp=33745617674&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745617674&partnerID=8YFLogxK
U2 - 10.1007/s11203-005-8113-y
DO - 10.1007/s11203-005-8113-y
M3 - Article
VL - 9
SP - 179
EP - 225
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
SN - 1387-0874
IS - 2
ER -