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Contrast function estimation for the drift parameter of ergodic jump diffusion process
- Publication Year :
- 2019
- Publisher :
- HAL CCSD, 2019.
-
Abstract
- In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter $\theta$. We suppose that the process is discretely observed at the instants (t n i)i=0,...,n with $\Delta$n = sup i=0,...,n--1 (t n i+1 -- t n i) $\rightarrow$ 0. We introduce an estimator of $\theta$, based on a contrast function, which is efficient without requiring any conditions on the rate at which $\Delta$n $\rightarrow$ 0, and where we allow the observed process to have non summable jumps. This extends earlier results where the condition n$\Delta$ 3 n $\rightarrow$ 0 was needed (see [10],[24]) and where the process was supposed to have summable jumps. Moreover, in the case of a finite jump activity, we propose explicit approximations of the contrast function, such that the efficient estimation of $\theta$ is feasible under the condition that n$\Delta$ k n $\rightarrow$ 0 where k > 0 can be arbitrarily large. This extends the results obtained by Kessler [15] in the case of continuous processes. L{\'e}vy-driven SDE, efficient drift estimation, high frequency data, ergodic properties, thresholding methods.
- Subjects :
- Statistics and Probability
Jump diffusion
Mathematics - Statistics Theory
Statistics Theory (math.ST)
ergodic properties
01 natural sciences
Lévy process
thresholding methods
010104 statistics & probability
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
0502 economics and business
FOS: Mathematics
Ergodic theory
0101 mathematics
050205 econometrics
Mathematics
Levy processes
05 social sciences
Mathematical analysis
Estimator
high frequency
SDE with jumps
Thresholding
Arbitrarily large
Diffusion process
Jump
Efficient drift estimation
Mathematics [G03] [Physical, chemical, mathematical & earth Sciences]
Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre]
Statistics, Probability and Uncertainty
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....b9e42f19e451712f3e63c9e113dd4083